For forehand:
First of all, I have to master weight transfer. I missed that point when was learning drive stroke. Now i't obvious, that drive's only(main) purpose is to master weight transfer during stroke)
That's what you were talking about, that my arm goes before my body. Also I noticed that sometimes ONLY my hand do the job. I conclude, that's all because of incorrect work of legs/hip.

For back hand:
Move racket to ready position faster. Use body as a bow to "load" the ball with more power and spin. Also it seems like I need to practice this stroke more, because I can't fix the ball, so hit it every time in different position. And I was told, that I should move my hand more forward than to the right. Should check this out too.

Also I will try to keep comfortable position of my body to stay relaxed before and after a stroke. I believe it will be possible after I correct my lower-parts(hip and legs) work.
Plus I really need to boost my legs. I lack physical strength and endurance. And even more, I found video about foot patterns, to make moves as minimal as it should be and as fast as it can be. Gonna work on it as well, but after the Holidays.

Regards,
Ami