You can't until you beat this game version of the elite four. Like in Ruby you wake up at home and head to the Professors house which is in the next town. While you are talking to him Professor Oak appears and gives you something called the Poketore (which is used to mark where hi level pokemon are in some patches of grass), then he leaves. You have to go to a place called Pal Park which is found by Surfing down the water route located in that town. When you get there you talk to Professor Oak again, who hands you an upgrade to your watch that shows which are the top three pokemon you found with the Poketore. Then leaves you talk to the person and you find that Pal Park had just opened. How it work every 24 hours you are able to move six pokemon for each GBA gamepak you own. (To do this in the loading screen there is a new opition that allows you to do this.) There are more down sides to this one you can just set the DS clock ahead the game will realize this and then make you wait 48 hours, two you cannot move Pokemon that have HM moves on them, so if you want to move Rayquelza you will need to unlearn Fly, Wailmer Wirlpool, etc. Here are another two issues I don't know about yet. In the Japanese version the game doesn't recognize US GBA carts, so if you have Japanese GBA games they might not register with the US version. Another is the multiple pack thing, you may have to go into the game and catch the six you transfered before you can put in another GBA pack and move another six. (It's not that hard the Pall Ball have a 100% catch rate but you have to catch all six to get them and you have to have a pokemon that surfs to get most water types.
As for the stage all I know about it is it is an expanded contest from the GBA games. (It hits me something like the ones from the anime Battle Frontier)
You also get four "escort" missions of sort that open up things. All battles are two on two, you get all the exp, your Pokemon are always healed after each battle so you can use them to level up. Three of them I don't know about, the first and the fourth is during the regular story mode. The second is in the cave of Doubt don't know what that opens up, the third is on steel island where you will need to have a spot open in you Pokemon rouster because he gives you an egg that eventually turns into Lucario which is a really good fighting/steel type Pokemon. (After a initial evolution.) The fourth mission is just to help you fight the two Admins so you are healed up afterwards for a one two punch. The first is an impressivly leveled up (compared to his last fight) against the leader of Team Galaxy then with being able to make a temporary reteat a fight to get/kill Dialga/Pelika. (After you get that pokemon go back into the shrine there is a hold item that powers up that legendary's moves, you will see the item behind the Pokemon right before you fight them.)
As I mentioned in my last post there is a trading center that is like the classified but I think most of them are rip off artists.
There is VoIP for the games but since I cannot speak Japanese I haven't been able to test this out. (Since most gamers will be Japanese.)
The battle pyrmid of this game has an Wi-Fi to it so you will you fight in Tournament type battles. A few Fire Red Pokemon are availvable on Northern Island after you beat the game. (Ferrow, Ratticate, Spearow, Ratata, etc I have run into)