First of all, I already updated to the latest firmware and also Pokemon Y 1.1; I managed to receive Torchic from the event and I also can trade through GTS. My problem is, everytime I tried to wonder trade, battle randomly, or trading with a friend, I somehow cannot connect with the player. In each case:
1) Wonder Trade
The game searched for trainer to trade for a very long time, ending with: "We could not find a trade partner for you... Please wait a little while and then try again!"
2) Battle Randomly
Same case with Wonder Trade
3) Trading with a Friend
I registered my friend, he registered back. He successfully initiated a trading invitation with me, I accepted. Then it seems the game tries to establish connection between us and fails to connect both of us
Things that I can do smoothly:
1) Connect with the Internet
2) Getting Torchic from event
3) GTS Trade
4) Seeing friend's, acquintance's, and passerby's avatar
5) Anything online in 3DS (updating, nintendo e-shop, friend code, browser)
Since I believe the only good connection I have is anything that doesn't need to directly connect with other players (GTS is done through a server I think?), I thought perhaps I have problems connecting to other players directly. Is there any solution to this? Perhaps any modification to the router needed?
Also, solutions that I have tried:
1) Resetting Router
2) Restarting my 3DS wifi
3) Activating StreetPass
4) Disabling Router Firewall
5) Getting my 3DS to Demilitarized Zone
But none worked 
I'd really appreciate any help here, thanks.