-" weak(not enough) tention of date jumper and it causes date changing 2days at the same time "
I has same problem, i had just changed part 625 and 623, you can get them in aftermarket (some $100 both) and problem resolved
Good luck
"Can yoi advise me how did you fix movement in the TC case and what kind of screw you used? "
Gen Screws 3135-5100, on Ebay