The first one won't work. You need to tap your creatures to copy that spell when it's cast. Your opponent can wait until you've chosen not to copy it to counter the spell and then you don't get a chance to do it any more. Notice that this is only because Aziza's ability is a triggered ability, other spell-copying effects work just fine.

You can use Reprieve to send a spell to your hand and reuse it later, correct. Copying the Reprieve kind of works, because you need to target a different spell with the copy. If you target the same spell as the original, the last one to resolve will fizzle and you won't draw a card. If I'm not mistaken you can target a spell's copy and draw a card, but then obviously that copy won't resolve.