Not sure if this has been asked before...but;
When you download your Mystery Gift (eg. Mew) and go to take it from deliveryman in PokéMart...can you reload to get the right nature?
Yes it is determined when received. I did it with the event Mew. Unless the event has a specific nature eg. the shiny legendary beasts. You may soft reset as many times as you want to get the mew of your dreams:). Just save before you talk to the delivery man then get mew check nature if it is not the one you want turn off the game and try again.
No, unless you turned off your DS while receiving (eg. Mew), so it is just all luck. You can only get one (eg. Mew) or (eg. Liberty Pass) per game card, but you could trade with somone who was lucky enough to get the nature you wanted.