Later, she will complain that I don't take her to the right places or do enough for her.
She then states her ex's take her to more expensive places and buy her gifts.
That sounds a bit like triangulation. She is pitting you against them so that you are in competition with them. It puts her in a one up position.
In response to my query of what makes her feel cared for in a relationship, she stated: "I will never tell you what I want. Then it's not as special if I have to tell you. If you love me, then you'll do your best and you'll know what I want."
That isn't cool. There is a big difference between wanting to know a person's love language and wanting a shopping list of things to buy or do. A lot of people recommend the love languages quiz. We have been married almost 17 years and we have both taken the Love Languages test to see what our primary love languages are. Would it be possible for the two of you to do that in a fun kind of way? That sounds abusive to me.
(1) Could saying "I don't know" to most questions be power play?
It could be a power play, it could be laziness, or it could be that she really doesn't know what she wants/feels/thinks at any given moment. Saying "I don't know" gives her power because it puts you in a position to guess or figure it out for yourself. And, if you guess wrong, then you get to be the jerk.
If a person isn't invested in the relationship, they could resort to using "I don't know" as a ploy to get out of being vulnerable and sharing with the other person. "I don't know" is a great way to dismiss somebody that you are trying to string along. I am not saying that is the case. It is a possibility.
And she could just be a bit clueless and out of tune with her own feelings. If somebody doesn't have much self awareness, it is going to be more difficult to talk about some things and "I don't know" is the honest answer.
(2) Is it reasonable to expect a partner to mindread what one wants/needs in a relationship?
NO! It is not reasonable at all. There needs to be real communication in a relationship. Mind reading is NOT real communication.
Somebody else mentioned reading between the lines. Is it possible that she has passive/aggressively told you what she wanted but you didn't pick up on it? I don't pick up on stuff when people are being passive/aggressive either. If a person is not being direct, it is very difficult to figure things out.