For Catacombs case, can we discard them and +3 Cards 1st and then put them into my hand?
Hey, I missed that possibility! Yes, if we assume that Catacombs doesn't lose track of the cards (as Dz was saying regarding how Dominion Online works), then yes, you could discard them, draw 3 cards, and put the discarded cards in your hand.
If it's the other way, that Catacombs does lose track, you could instead choose to put them into your hand, then fail to discard them, and draw 3 cards.
In either case, you end up drawing 6 cards!
EDIT: Just tested it online. If you choose both options, the client doesn't let you choose to discard first, so you end up discarding the cards. Pretty sure that's wrong. EDIT AGAIN: You have to do it in order, so this would not be possible if you have to choose options first.