No, you don't have to. It depends when you get Shaymin from the toys r us giveaway.You get the gracidea flower in floroama town.You have to look real carefully to see if the lady was there before
you do not necesarely have to beat the elite 4 to get arceus mostly because you can only get it via hack.
You get it after you beat the elite 4.
to get into n castle you have to beat the elite 4
No you can trade anytime before beating the elite four.
after you beat the elite 4