1 - She might, but she has not so far.

2 - We have no idea. That goes for both of #2.

3 - He had to work for it, and Annie had misgivings about being a Warrior. I assume those misgivings held her back. I don't think it was necessarily feelings about Eren. Just in general, she's not as callous as she pretends to be.

4.1 - I don't think she does. She talks a lot about just going with the flow and that it's remarkable when people don't, which seems to indicate she's another person who is just swept along.

4.2 - She's probably pretty knowledgeable, but I don't think she's a schemer. Annie's primary motivation seems to be obligation to her father and not any grander purpose. Without having a higher purpose it's difficult to see her planning for anything other than getting home in one piece.

I stand under correction but I think the crystallization of another character happens in chapter 101-3, someone from the tyber family, Eren's Titan hold a crystallized character looks like he is going to consume it.

I remember the speech her father gave her, I just figure she had an end game. (Probably a Lost Girl after all.)

I just hope she doesn't get killed off screen, I want a fight between Mikasa & Annie as it was just teased or maybe end up working with them to get home to her father (a bit of a Vegeta Ark not good nor bad - questionable at best.)

Given what we learned in 103 I think Annie's crystallization is kind of like Koro-sensei absolute defense form...

Though I have doubts if Annie can actually get out by herself.

He knows what's going on around him, Annie on the other hand seems to be in deep sleep, perhaps waiting for someone to wake her up (Reiner told Bertolt that they would come back for her), or she's sleeping for a period of time.

Which begs the question of how someone can get her out?

And will she die because of Ymir's curse or does that form prevent it?

The other person who crystalized was conscious and aware, that's why I am assuming that Annie is aware as well.

The only problem is this other person has a pelicular titan power that would allow a way out while Annie doesn't have it.

Is the crystallization in her titan form because I saw marks on her face while she was in it or human form?

I believe she might be able to get out because Eren can use his coordinate powers in human form so why wouldn't she be able to also, look at Reiner he can choose when to use his healing powers to avoid arousing suspicion.

Technicaly you could say she never left her titan form, we can consider the crystal as Annie's second transformation.

However since Annie hardered all around herself, she can't get out or trigger another transformation because she's stuck in place plus they put her underground.

This other person titan's power acts very different from the norm and could free themselvers despite being stuck in place, that's why I believe it's more realistic that Annie is still stuck in the crystal.

(even if it would be awesome if she freed herself and joined the fight)

About Eren's coordinate powers, I can't say anything else but read the manga.