White to move and win in both cases.
Hint for 1: you probably heard of this from Josh Waitzkin
Hint for 2: cartoon character trying to cover the holes in the boat with their fingers and running out of fingers.

For 1., pushing the e pawn looks interesting. It would be defended 3 times with 1 attacker. There's also a possibility with the queen and bishop on the diagonal, but I'm not seeing it.

For 2., it may start with Rb6, Rc8, Rxb5. Then maybe Rc7 to defend the queen, Rb8+, bad news for black. There may be a way out though by simply blocking with the queen at the beginning. Probably better is Rxe6, queen can't take, maybe Rc1+ or something, white king moves into the attack, perhaps. Re8+, Qxe8, Qg7 (mate?) looks hard to stop at some point.

7729543
1. Right. Josh Waitzkin hint was about "the space left behind". I removed the last move indicator from this one, and it was queen going from d8 to b6, leaving the bishop undefended. After e5, black loses a piece (well, the computer shows a line where black can give up two pieces for a rook, but still be completely lost). Nd5 doesn't work since after Nxd5 the queen is attacked by the white knight and the bishop is still hanging on e7. Black came up with h6, but this loses to exf6 hxg6 fxe7. My opponent then attacked the e-pawn with a rook, I took on g5 with the knight and when he took on e7 with the rook, I put the queen on h5, forcing resignation.

2. Rb6, Rc8, Rxb5 is probably winning anyway, but Rxe6 is the way to go. Even if black plays Rc1+ Qxc1 Qxe6, the resulting endgame is winning for white, as the queen can quickly pick up the b-pawn by checking the king. Rc8 is a better move for black as otherwise Re8 would force the queen to take and allow mate on g7. After Rc8 the computer at first suggests h4, but I guess that's just computer being weird as Re7 instead wins the queen on the spot (my opponent went Qf8, missing Qxh7#).