Go back to Lustersand Town and talk to Kronz.
Earn your badge there.
If that doesn't work, head to Guardia Town and battle the gym leader there.
PM me your saved file.
Include details of your error (so I will know what I need to fix).
2. Because Shadow Lugia isn't important in the LoG storyline.
4. Because, in the real timeline, he was controlled by Shadow Lugia in Reign of Legends.
Of course. That's the purpose of the second floor, right? o.0
Anyway, I made that accessible because my bros and I used to play the game together, and we tend to do link battles and trades.
Keep in mind that, if you trade with other games, the PKMN would be really different.