Merrill - “It's a Keeper's job to remember.”

Wanting to get your family out of poverty and improve your living conditions is not obsessive behaviour.
Which completely misses the point I made. With very few Darkspawn currently down there, the chances of running into them and becoming infected by their blood is at an all-time low. If you don't bring your sibling along, no-one in the entire expedition gets infected at all... so clearly it's not nearly the suicide mission you think it is.
Which all the information they'd gathered suggested did exist... and which they actually did manage to find.
That does not qualify as an obsession.

You keep using that word. I do not think it means what you think it means.
Again, how does Merrill actually plan on doing that?

She's fixing up a busted old mirror in order to bring back a piece of Elven history, but she has barely the foggiest idea on what it does. How does she think that would have any meaningful impact on the day to day lives of Elven people throughout Thedas, whether they be Dalish or City Elves?

In comparison, Hawke used the money from the expedition to not only improve their lives and their families, but according to Aveline poured a lot of money into Kirkwall in order to try to help improve the lives of other people in the city. Hawke also spends their free time actively clearly out bandits and thugs who plague the city, which has an overall more positive impact on their community.
Gaspard and Briala discovered what the Eluvians are and the existence of the network, that they recognise could potentially upset the balance of power in Thedas if someone managed to gain control over it. When they make this claim, they can do so with both knowledge and authority on the subject matter.

Merrill on the other hand does not know any of these details. She doesn't know what Eluvian does and only can guess at it. Her belief that it could change things for the Elves is completely unfounded because she doesn't have any of the facts necessary to make such a wild claim, even if we as the audience know she's right.

From her point of view, she's trying to give a HAM radio to a group of starving people and hoping that it'll change their lives. It doesn't matter that it's actually a friggin' Stargate, she thinks it's an extremely fancy way to communicate across long distances... so how does that help anyone?
By using shards from an already-existent Eluvian that was destroyed to restore it to full functionality.

Since it still contains components from the original device, one can't even employ Theseus' Paradox over whether an object that replaces all it's components is the same object anymore... it's still the same Eluvian as before, Merrill simply reassembled the pieces and put them in a brand new frame.
So her familiarity with Nyssa (who works practically on Merrill's doorstep) and Philomena (a crazy woman who throws things) someone proves that Merrill somehow knows all her neighbours, despite her own admission that she barely knows any of them?

You also seem to have forgotten that Merrill protecting the Elves occurs during the Mage-Templar War, years after the events of DA2.

Merrill gives up trying to fix the Eluvian entirely following the death of Marethari in 9:37. After losing her clan (either to death or banishment), Merrill makes the decision to finally interact with her neighbours and focus her efforts on helping the Elves of her new community... which is completely in line with what we later learn she's doing by 9:41.

WOT does have some lore hiccups when it comes to dates, but overall the information is far more solid than your headcanons.
Which I have already disproved by pointing out that the entire Free Marches are completely packed with refugees. Trying to make a life outside of Kirkwall is not an option, nor is something ever suggested by any character, with the only time they even do mention going elsewhere it's to try another city.

Hawke never even makes any suggestion they could use the money for the expedition to escape to the country. Stick to facts from the game, not your own headcanon.
Not sure what you're even rambling on about here.
Except that Hawke's money didn't fund the entire expedition, as we're told that Bartrand had sunk a lot of money into the expedition but was coming up short. 50 Sovereigns seems to have been the minimum amount that Bartrand needed to get things actually rolling, which was how Hawke was able to bargain to become a partner.

So while more money than most refugees are able to scramble together, it's hardly an impressive amount of wealth. Later in the game, we can shell out just over a third of that (15 Sovereigns) just to buy some decent pickaxes for the miners at the Bone Pit.
Except for the part where it demonstrates that Merrill explicitly ignoring someone because her overwhelming curiosity got the better of her. This is one of the countless many times depicted in the games that Merrill ignores those around her trying to warn her of the danger, because she doesn't want to hear what they're saying and thinks she knows better.

Her refusal to heed the advice of Marethari, who tells her to give up her fixation on the mirror and avoid the cave containing Audacity, shows clear obsessive behaviour. Marethari values Elven history just as much as Merrill does, but after the death of Tamlen (and Mahariel), she recognises that the mirror is too dangerous and some things perhaps should be forgotten.

It's not that Marethari wasn't curious about the Eluvian, as in the Dalish Origin she even asked Duncan about sending hunters to study or recover the mirror. When he informs her that it had to be destroyed, because it was corrupted and could cause others to become tainted, she immediately drops the issue. Marethari recognised that it was potentially dangerous and that she had to keep her clan safe from it, which is why she argued with Merrill when she learned she'd recovered some of the broken shards.
Gaider confirmed that Merrill was restoring the broken Eluvian by taking the mirror shards and placing them in a new frame.

No-one was arguing that point, unless you're being deliberately pedantic and somehow don't understand that "Restore the mirror" is synonymous with "Reconstruct the Eluvian", when either Merrill uses both terms interchangeably to describe what she's doing.

Likewise, no-one is arguing that Marethari wasn't wrong in her mistaken assumption the Eluvian would free the demon or that Merrill would make a deal. However when you consider how easily Merrill fell under the sway of the demon in "Night Terrors", you can understand why Marethari might have been concerned about this possibility.
Yeah it does, try again.
Which completely misses the point of what constitutes an obsession, the completely different goals that Hawke and Merrill have, that Merrill's behaviour is self-destructive and negatively impacts those around her, none of which apply to Hawke.
Only if you don't understand what "obsession" actually means... buy a dictionary.
Going into the Deep Roads only three times in one's entire life is not enough to qualify for "unhealthy behaviour". Spending several years trying to fix a busted up old mirror while neglected everyone around you and your own health, definitely is.

As I mentioned several posts back, Merrill is actively lying to a romanced Hawke in that scene, made obvious by how her extremely noticeable pause about why she's going to her old house, before coming up with an explanation that she has left some things behind (such as a mirror).

It's obvious that Hawke knows too, since the diplomatic response even has them say that whatever she's doing, they hope she's careful. That's not something you say to someone you're assuming is going back for some old hairbrushes and shirts, they know she's going back to work on the mirror.
Sorry to disappoint you, but your bizarre headcanon doesn't prove anything either.

There is no evidence of Hawke having obsessive traits, compared to the multitude we see from Merrill. You're wrong, let it go.