For me, that depends.
For example, if you caught a Heatran on your Platinum and you have cloned/traded it around and you decide to rebattle another Heatran, then no. I would not allow anyone to trade different Heatran with the same OT/ID.
If you caught a Cresselia pre RNG on your Platinum and she has an awful nature and was never traded away, you may rebattle her to capture a better one.
One legal legendary per game, basically.
Azure flute, no. Hall of Origin Arceus is prohibited. Find someone with the wondercard to do a SR request. I do not want to get into whether if hacked wondercards are allowed here or not, so stick with legit wondercards.