League of Legends (LoL) Question: Question about lores in the present below. Where should I ask them tho?

I will say this before starting, I'm not to par with everything regarding everyone's lore, so I will surely miss a lot of things

I guess for the first question I could say Illaoi, but that's a big stretch: actually we don't know if she was chosen by Nagakabouros to serve her as a priestess or something like that, but the whole doctrine or religion (call it as you prefer) is based all on commitment to live your life at the best. Nagakabouros gives her powers to Illaoi to test pepole to see if they are following this kind of path. But again, it's a big stretch, nothing comes to mind when I think at some champs that acquired their abilities because "passion, love, commitment"; or they are demi-gods or they are nearly-divine beings or they are humans that have a precise objective in their mind.

I could go by classification to see why they have the powers that they have:

• darkins (aatrox, rhaast...): by recent lore they should be ancient shurima weapons, so their power is innate
• vastayans (ahri, xayah...): again, the magic powers should be innate in them; their objective differs, but anyway they didn't learn what they know to do just because they wanted to learn new things.
• yordles: eh, maybe here I can find a couple of examples. Heimerdinger just wants to invent stuff that then magically helped other peoples (for example his turrets: he just wanted to give some kids something to practice baseball, proceeds to create something that drives away A ******* GIANT), ziggs loves explosions (again, saving by accident some peoples because why not). But this two lives in piltover, not bandle city. In bandle city I guess yordles like tris or teemo do what they do because they were entrusted to do so?
• demi-gods/ascended (anivia, nasus...): they are literally gods. An argument can be made for some ascended (like maybe nasus?), but unfortunately I don't know much about it.
• voidborns/void-related champs: voidborns were born like that, void-related champs is because the void gave them powers. Malzahara could have been another example for your question, but recent story rewriting changed that.
• targonians: ok, maybe the targonians fit more inside your criteria. I think they acquire their power because they demonstrated their willpower to some gods or stars or whatever by climbing mt. targon. I'm pretty sure for Pantheon, a bit less for the others
• shadow isles (hecarim, kalista...): eh, magical powers of death, just this
• UHHHHHHHHHHHHHHHHH: welp, here is everyone else. Unfortunately the others have, as I stated before, very clear objectives (camille works like a piltover spiderman, lucian kills every ******* spirit because thresh is a douche) or they are like that just because (jinx likes to blow everything up, braum is a nice guy, kled hates everyone, thresh is a douche)

Even if it doesn't seems so, your criteria are pretty limitative, that's why it's difficult to find someone D:

Now about the second question: it's not really clear, but for what I understood it ask for a really deep knowledge of everyone's lore, thing pretty impossible for me at least. Maybe the new soraka's lore should be at least a minimal answer to your question.
Maybe the voidborns can fit into the answer too, they want to destroy everything, they found runeterra, now they want to destroy runeterra. Pretty straightforward.

And now the last question: unfortunately we have to base everything on the stories that we have, so I can affirm centainly that everyone's lore is incomplete rn and we can't know everyone exact position. Maybe you can just theorize where/what the champ is/is doing. For example Illaoi is just there in the temple doing priestess things, tahm kench is probably eating someone somewhere...
If you really want to make your own champ that has some kind of correlation with someone, you should find open stories (like annie's as you said), where there isn't a clear end. You can always make something up at some point of the story of other characters too, look at sylas's lore for example. We never knew that lux had a "special" friend, now we know it and we know who it is. You can chain (no pun intended) your story to everyone by just thinking outsides the stories we already know.

Hope it answers (or helps someway) your questions!