1. Why is Xavier alive? In Xmen 3 he was killed by Jean.
Agree. They gave a silly explanation in some interview that he transferred his soul and mind into his twin brother's body (the one we saw in X3).
2. Why is Kitty able to send someone's mind back in time? Last time I saw her she couldn't do that.
It's simply something they haven't shown in the other movies.
3. Why should the DNA of Raven allow the sentinels to adapt other mutants powers? As far as I remember Raven couldn't adapt other mutant's powers, only other people's look. Much better in that direction would have been Rogue's powers, but since she wasn't born yet in the 70's, they could only use Raven.
Agree. But then again, they could have been given rogue's powers in the future, since these Sentinels are Mark 10 (or whatever number) and they were upgraded only in the future.
4. Why has Wolverine in the future his adamantium claws? In Wolverine 2 his adamantium got extracted.
Remember : Magneto can control metals, he might have got them back for him. Showing these details isn't that important.
5. Why is it possible to build hightech flying robots in the 70's?
It's a fantasy science fiction superhero movie.
6. Why could Magneto give orders to the sentinels? Sure he could use his magnetic skills to make them do what he wants, but he went beyond that and actually gave them orders and they obeyed it.
Trask already told the president that the sentinels aren't metal, so Magneto can't move them. Magneto got the plans and studied every wire in those sentinels so he knew exactly how they work, thus, he introduced some metal in them to reprogram them.
7. At the end Raven saves Wolverine from Stringer's grasp, so he didn't get his adamantium claws, and all that happened in X1, X2 and X3 didn't happen, so that Jean and Scott are alive again. I have the strong feeling that all this incredible time-travel-story had only the goal of getting Jean and Scott back alive. I could understand the desire to undo the awful X3, but the price is high as it means to also eradicate the awesome X1 and X2''s stories.
Well. Wolverine can get the Adamantium again.
The movie was made to fix the catastrophic damage done by X3 and some continuity errors in the whole franchise. They clearly want a neat restart and follow Marvel's steps in building a universe.
And you can't say X1 & X2 were eradicated, no matter what, for us the spectators, we have seen the different alternate realities already as a whole entity, it's like back to the future where several timelines have been rewritten in the same movie.