How to properly get involved in the lore?

I'm not entirely sure what you're asking for. Do you want to learn about this universe or find a way to make the games fun to you again?

The replayability of Inquisition is really low. But Origins has great replayability: playing a different origin and seeing how other characters react differently to your race/origin/gender is really great. Also seeing how these unique stories develop is really satisfying and give a lot of insight you missed on another origin. Like finding that a guy you saved on your first save was actually a rapist

No, not as much in origins, no. And it really doesn't make much of a difference. I played as an elf and as a dwarf, and there is almost no difference. Some people acknowledge your race, there are very few dialogue choices based on your race, but that's it. The game stays mostly the same.

In Origins, you meet again the people you met at your origin story, people treat you differently, not letting you walk into places depending on who you are.
If you are a noble, the others nobles recognize you, and the fight against Arl Howe becomes much more personal. Also, you can become queen/king. 
If you are a mage, going back to the mage tower feels far more different, and you get more insight on Jowan
If you are a city elf, you'll find out the guy you possibly saved last game was actually a rapist pig. Not to mention the city elves will treat you differently and it might have a different outcome
If you are a noble dwarf, the quest in Orzammar feels totally personal, because everybody knows who you are. 

It's far, far different than in Inquisition. In Inquisition the best you got is a table mission. It's even funny that your DALISH CHARACTER doesn't seem to know a thing about elves, gods and the elven language.  

He does get some special dialogue choices, yes, but like exploring the temple of Mythal the difference is almost non-existent. He still lets Morrigan translates the texts as if he couldn't read, and even explaining to him what each god is, it felt very immersion-breaking. And no, I didn't feel the Inquisitor origin is much discussed. Like I said, at best some few lines of dialogues. 

Origins is probably a good basis on which to base your investigations. Play through each origin story at least once, even if you don't then go on to complete the entire game. This gives an insight into the various cultures from a personal perspective and you may find more enjoyable than simply reading through multiple codices or books.

However, there is a caveat that you may subsequently find aspects are changed in later games; a prime example being the 3 mage rule among the Dalish which absolutely did not exist in Origins and was only introduced in DA2 to explain what happens if a clan does not have a First to take over as Keeper when the current one dies. So if another clan had more than 3 mages they allowed the other one to adopt one of their extra mages, not the clan kicked out the surplus mages because they were terrified of the prospect of possession. (I harp on about this a lot). It is aspects like this that can actually make it better not to know too much lore.

Anyway, if playing through the origin stories wets your appetite for more, then select a subject you are interested in and check it out on the Dragon Age Wiki. This is mostly accurate.

If you enjoy reading and don't mind spending the cash, then there are the lore books World of Thedas and World of Thedas 2. The first gives information about the various nations, races and cultures throughout Thedas, the second concentrates on fleshing out some historical characters and then giving additional information on the various companions, advisors, enemies and agents that can be found in all 3 games and their DLC, plus some additional characters from the early comics and novels.

Finally, there is the Core Rule Book (available as hardback or digital download), which brings together information that was originally issued with a table top version of the game around the time of Origins. Whilst it is intended for people wanting to RP a table top campaign there is a lot of lore and history in there not found in the other two books.

Morrigan says the same things she would have said to any Inquisitor. Like I said, I played with a dwarf and it felt mostly the same. 

And yeah, like I said, most of these are actually just a few dialogue lines, nothing that has actual impact on the story. 

For the size of the game, this list is indeed low, since mostly are just VERY, VERY, VERY forgettable scenes of absolutely no importance that are there just to remark your inquisitor is an elf, but don't have any impact on the story overall. Hell, even being a dalish, you still have to "gain the trust of the dalish clan", LOL. Also, you make very poor excuses just to not admit that Morrigan's dialogue doesn't change. For the size of the game, yes, that is a list with very few moments, especially when you compare to Dragon Age: Origins, which was a much shorter game, but your origin was much more discussed, developed and with ACTUAL IMPACT IN THE STORY, WHICH IS WHAT I'VE BEEN TALKING ABOUT SINCE THE BEGINNING. Imagine being so afraid of being wrong that you can't admit Origins has much more replayability in matters of origin stories than Inquisition. 
90% of the dialogues you're listed are there just to remind your character that he's an elf, nothing less. 
I can make a list probably much bigger of interactions in Origins, the difference won't be in the size, but that these interactions are actually meaningful and change a lot depending on your origin. 

I don't give a shit if Lavellan can "explain believes" during WPHW, I've played the game as an elf and as a dwarf, and I can AFFIRM the game stays mostly the same with almost no replayability value. Especially as a dwarf, since the game has at least some main quests that involve elves. 

I did like driving a sword through Howe as a human noble but that happens regardless.

I mean your Origin might change your characters perspective on certain events but that doesen't neccessarily impact the choices you have. Though some of the boons offered by Alistair are Origin specific but that is one of the only examples ( and takes place in the epilogue)

No, Iddy's right. The origins in Origins don't really impact how the plot actually plays out. You always have the same options on the main story's decisions, regardless of origin.

It does effect dialogue some characters say to you and maybe you learn some details you wouldn't otherwise. Or see a less rude side to people, like the hahren of Zathrian's clan if you are dalish. Having played through the origin gives you as a player a different piece of the world's lore, and that influences your mindset, yeah. But the mechanic that that impacts is just getting extra/different dialogue from npcs, just like Inquisition.

Playable prologues = good, bring them back. But don't act like Inquisition had no acknowledgment of the Inquisitor's background b/c, as that extensive list showed, it did.

Uh, no, not really. The only real effect it has is 10 points loss if you're not human. No big deal. You don't need the noble's approval for anything other than denounce publicly the woman attempting the coup (and even that isn't needed). The only thing you need to get the "best" ending is proof against the three of them, and that's it. Easy as pie. 

Actually, I'm pretty sure there's an elf-only option to try to speak with the sentinel spirits in Trespasser, in addition to the Well of Sorrows option. (Or maybe in place of it, only there for an elven Inquisitor who didn't drink? Not sure.) The attempt doesn't work and the spirits still attack you, but its an elf-specific dialogue choice. My canon is an elf that has Morrigan drink, and I remember trying to talk the spirits down using a dalish greeting and failing.

I think you can try speaking elven to them but they still attack you, as opposed to a non-elf who I assume wouldn't even try.