"If you're below 1000" a few seconds later "you'll quickly realize that it's too late because black has a checkmate in eleven moves". If you're 1000 or below, your opponent should be too. So it means that your opponent is probably one of these stockfish user.
1:23 Won't it be better if you just put your other rook on the same rank as well? Now the queen is pinned, if king moves you get the queen free of charge and even if she takes you can just take back and be in the same position(granted your rook will be on h3 not g3, but c3 is still available
For the last one: Once played Ra5, black will block with Qa3, Rxa3 trades the queen for the rook, white wins with 2 more points of material, easy because the other rook attacks the pawns and the black king is too far away, after that, just do single rook checkmate.
For puzzle 1 I think 1. Rh3+ is better than 1. Rh1+ because at the end of the line you get to immediately pick up the knight with the first rank rook. For puzzle 2 you forgot to look at what happens after 1. Rb5+ Ka1 2. Rc1+! Ka2 3. Rc7 Qa8 4. R5b7 Qh8?! . What do you play now?
The third trick: as I see you don't search for the easiest way, do you? The easiest way to win is not Rb5 but Rb8 Check! If the King goes to a1, than White play Ra5 Check! The only way for Black is to Block this check by the Queen - Qa2. White play Rb to a8. The only thing, that Black can do is to trade the Queen for the Rook at a5, and White will have the free Rook and win! If after Rb8 Black play Kc1, than White play Rc5 Check! Black play Kd1. White play Rb1 Check! Black play Ke2. White play Rc2 Check! Black play Kf3. White play Rb3 Check! Black play Kf4, and than White take The Queen and GET TWO free Rooks!
qg8 is a even more blunder because the king can just take the queen, the pawns can’t protect the queen as the pawns are on the 7th rank, therefore leaving the queen protectionless
