What is a WEP key?

It's a type of WiFi password, from what I know. If you're playing the 5th generation and have a different kind of password, you can access other types with a DSi or 3DS, but not a DS Lite or DS. The option for others should be in the Advanced Settings. If you're playing 4th generation, there's nothing you can do with a type not on the original DS, sorry.

As for a GTS, it's short for Global Trade Station. Basically the WiFi area in the game. You can trade and battle with it, and if I remember correctly, share/mix records? I'm not sure, though.