Links between Andraste and Mythal/the Evanuris?

Well, I wouldn't be quite so sure about that. It depends on how much store you place in what is contained in the two World of Thedas books, particularly WoT2 that came out after Inquisition was released (but before Trespasser). Here are some of the connections:

In addition to what we found in game in the Temple of Mythal there was an old elven poem from which a Denerim lullaby is said to derive via an Alamaari War Poem. Andraste was an Alamaari so it is possible the war poem was introduced during her campaign. The elven version from the Temple of Mythal is lamenting what they have lost as a result of the Wolf's fight for freedom. The word Glandival appears there in connection with that struggle and it seems likely it means "believe", in this case the line is "when we could not longer believe" (in the gods?)

Andraste gives Shartan her sword that was originally given to her by her mother. It is not absolutely clear if it already had a name or Shartan renamed it but the sword was called Glandivalis. That is an elven name and based off the poem means "Faithful" or "Believer". The Chantry would say it was an indicator he was her disciple so he believed in her or the Maker. However, the elven version in the Canticle of Shartan states she gave it to him after he saved her from defeat at the Battle of Valarian Fields with the words "Take this, my Champion, and free our people forever." Notice there is nothing about him being a faithful disciple or believer in the Maker but a believer in freedom, who joined his forces to hers in that cause. So, it is entirely possible that the translation of the name Glandivalis means "Blade of the Faith" (in Freedom). This was a title that Drakon later appropriated to himself after allegedly receiving a vision from Andraste that he should be the one to spread his version of faith in the Maker, or as Ameridan put it "simplify" it from the multiple cults to Andraste and the Maker that existed in the south prior to his reign.

In the subsequent Canticle of Apotheosis detailing Andraste's betrayal and death, Shartan is not named directly but only as "the Liberator", likely to conceal his identity after the Canticle of Shartan was removed following the fall of the Dales, although may be he was now called that generally in view of the previous words of Andraste. He was trying to rescue Andraste from the pyre together with a hundred of his followers. Note that when the human followers failed to help her, the elves did. No wonder the Chantry wanted to keep that quiet after Orlais had stolen the Dales from the elves, which Maferath gave to the people of Shartan despite him no longer being around to claim this in order to honour the wishes of Andraste. It would seem even Maferath didn't dare go against the will of the Maker in that. Still the title of the Liberator again points to Shartan being a believer in freedom rather than simply faith in the Maker and this in turn does make him a mirror of Solas.

The preface to the Canticle of Shartan also says that there is an old elven folktale about a trickster warrior who fought against tyrants that human scholars believe may have become mixed in with the story of Shartan. I have no idea why the writers wanted to make this connection between Shartan and Solas but it did result in numerous fan theories about how Shartan could have been Solas (hardly likely since Shartan was killed trying to rescue Andraste from the pyre and then his body burned as well). However, it is possible Shartan knew the story and used it to inspire his followers. This would suggest there was more than one tradition concerning Fen'Harel among the slaves of Tevinter that later occupied the Dales but either his name was dropped from the story at the insistence of the Keepers that it related to someone else, or by Shartan's time the link to Solas and his rebellion had already been lost. Still, it does seem odd the writers would want to hint at a connection between Shartan and Solas in a rebellion to free their people from slavery. Which immediately makes you wonder if the later exchanges between Shartan and Andraste came from the original folktale as well, particularly the injunction to Shartan by Andraste to be a perpetual champion of freedom for their people.

There is also an interesting aspect from the Canticle of Apotheosis that suggests that Andraste was captured by Tevinter after Maferath suggested she go into the hills to consult the Maker as to his will at a "pool of silver where they say the Voice of Heaven can be heard most clearly." This was meant to be somewhere near Minrathous because in this version the Battle of Valarian Fields occurred just outside the gates of the city. However, in the version we learn in DAI, it would seem to site of this battle was much further south and her army never got that far into Tevinter proper, certainly not as far as Minrathous. After the battle she stopped for a time at the fortress of an ally in what is now Nevarra and it would seem that having such a close shave in that fight, Maferath thought it would be extremely unwise to venture further north into the heart of their enemies power. However, Andraste was determined to continue with her crusade and so Maferath did a deal with Hessarian to deliver her into his hand in return for being allowed to keep what they had taken from Tevinter in the south. Since the Imperium had already been struggling to hold many of these outposts and he was having to deal with multiple slave uprisings across the Imperium inspired by Shartan's efforts, Hessarian did the deal. She was handed over to the Archon's forces in Nevarra, which explains why there was no army of barbarians outside Minrathous that could have saved her but only a small force of elves led by Shartan, probably his followers actually in Minrathous, who attempted her rescue.

However, if this latter version of the story is the true one, where does the "pool of silver" (clearly a lyrium pool) fit into this? Could this be another transposition of an earlier folk memory of Mythal and her betrayal? Was it perhaps the teaching of a southern Augur who had asked spirits of the Fade for a vision of the betrayal and got the one of Mythal rather than Andraste? In both cases, it seems likely it was the husband who betrayed her.   There have been strong hints that the betrayal of Mythal by the other gods was in connection with either lyrium or red lyrium and she does appear to have been in control of the lyrium mining operation.

Further thought, why did Andraste promise Shartan the Dales for his people, an area that seems heavily associated with Mythal and Fen'Harel (judging from the number of giant wolf statues around the place) but certainly with the elves in general. Was Andraste aware of this? If the sword she gave to Shartan came from her mother, was this something her family had simply looted from an elven site or was her mother or one of her ancestors an elf? If Andraste had elven blood in her veins that would certainly explain her strong connection to the Fade. It goes without saying that Andraste was a mage and the southern Chantry suppressed this information. Dorian confirmed that up in Tevinter this is what they believe. Also, if there were elves in her ancestry it would explain the elven connection in the Alamarri war poem that would be hard to explain by humans re-purposing human ruins because they couldn't speak or read elven. However, there was evidence of humans and elves cohabiting the ruins in the Brecillian Forest, not just humans moving in and occupying them after the elves had left, so this could have been the case elsewhere in ancient times, particularly as the Dalish recall some of their people having close contact with humans, that the Keepers teach had an adverse effect on the elves both in their longevity and behaviour, so that is when those faithful to the gods chose to withdraw into Uthenera. Presumably, those not faithful to the gods chose to stay among their human friends, inter married with them and thus any children of the union lost any outward indication of their elven heritage, only likely retaining it in their blood, the first human Dreamers.

I thought the question was about a connection between Mythal and Andraste. You say no, and then agree that the tales in the Chant are likely cultural appropriation. So, whose culture were they appropriating? My lengthy post was to give examples of how earlier stories could have found their way into later Chantry teaching, not just the Canticle of Shartan, and the evidence for why there is a link between the Alamaari and the elves that could account for it.

Actually I would say it at least gives a possibility of a link considering that Andraste pre-dated the formation of the Chantry by nearly 200 years (starting with her birth and early visions) and there are definite connections there. It doesn't mean that Andraste herself was Mythal or anything like that but that there was a likelihood the stories of the former could have been influenced by a vague folk memory of the latter.

Also, you connect the cultural appropriation in the south with the Tevinter Imperium period, implying they were the ones responsible for it in the south as well as the north. It is debatable just how much influence they had that far south and the barbarian history in the south developed for the most part independently of the human kingdoms in the north. They have completely different magical traditions (although they do bear similarities with Rivain suggesting perhaps a common origin). The Imperium tended to completely erase the references to earlier elven culture when they appropriated the ruins and there is no evidence there of elven legends surviving and entering their lore, although there does now seem some sort of link between the Old Gods, that they only adopted en mass in the north much later than the retreat of the elves into Uthenera. The southern barbarians may have retained more memory of their links to the elves (the Fog Dancers of Seheron certainly acknowledge it) but Drakon's purges and then centuries of Chantry influence likely all but eradicated it.

You haven't read WoT2 have you? There is a completely different version in there, part of which was reproduced in DAI. She was never a Tevinter slave, as in being held up north in Tevinter. She was captured by Tevinter during a military campaign in which her father was killed but she was already married (or promised in marriage) to Maferath, so technically she was a prisoner of war and potential slave had they taken her north to sell. However, she was ransomed by Maferath because their marriage had been a political one and her tribe only felt allegiance to her not him. He had needed their support to fight back against Tevinter, so he had no choice but to buy her back. There seems a strong suggestion she acted as their Augur giving spiritual advice and guidance, whilst he was the political leader who usually managed military affairs (an arrangement we see among the Avvar - an offshoot of the Alamaari - in JoH). This is why initially their crusade was a success because their aims harmonised with one another and he had the backing of his tribe, her father's tribe and her mother's tribe to call on for support. Then after the near disaster of the Valarian Fields, he decided their crusade had gone far enough.   They never got as far as Tevinter proper, Maferath calling a halt in what is now the border between Nevarra and Tevinter.   

This was a secular history from universities that had made a study of the matter from a non-religious perspective and thus not influenced by Chantry propaganda. The same was true of the history of Drakon. Whilst they may have got some details wrong through incorrect interpretation of the facts or incomplete historical records, I think we were meant to assume that the majority was for the most part true to what actually occurred as opposed to what the Chantry would have us believe.

The bit you have stated as being the only important information is actually taken from Chantry propaganda and religious dogma, not historical records.

I wonder how Andraste will be portrayed in Tevinter - will she be a brunette compared to the Chantry Blonde and Ferelden redhead?

The theory that I find most probable given the timeline and the available information is that Andraste was born as the mortal vessel of Dumat after he was slain at the Silent Plains. Dumat's death throws were so violent that he killed seven Wardens when he finally died for good, so no one knows which Warden dealt the final blow or if that Warden died as a result of killing Dumat or if it was just Dumat's death throws that did it. The Dark Ritual had to come from somewhere.

The forehead brand might be "decorative" or it gets healed/removed when the reversal succeed.

As for how they attract one, they clearly aren't attract it from the Fade. So either someone is sommoning one in the room or there is another secret Cassandra didn't reveal (she really didn't reveal much irc).