Another...
First one, 8. Qa2, Kd1 9. Kd3, is mate next move Qc2 or Qe2 depending on Kc1 or Ke1 from black
the second puzzle/moves is not great. many of the moves are not good, and white should not lose either pawn at all! it is a won game for white but as you have it, it ends in a draw.......RxQ, KxR, KxR
I think black might last slightly longer in the first puzzle if he plays 1... Rc8+ and attacks along the file rather than the rank.
I think black will struggle to save the rook if white after blacks capture plays the rook to g1, g2, g3 or g4 threatening instant mate. However 13. RxR will also win as 14. Kd7 leads the pawn all the way to promotion. Some moves before this could as mentioned above be played better.
Oh sorry. Looks like I didn't do my homework.
According to a tablebase, black can last for 16 moves in the first puzzle:
Actually it's a win for white. RxQ Rg1! threatening backrank Kh6 (forced) Kxe8
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