Can you join a full server?
No, can’t transfer for free. Your brother could just keep trying to hope for a slot to open up. That said, unless you plan to WvW together, being on the same server doesn’t matter anymore. You can both still be in the same guild and hook up in all the PvE content. I play with my kids occasionally too and they’re not even in a guild…I don’t even think they’re in the same world either. Not sure about PvP if you have to be in the same world.
If you WvW a lot, you probably won’t be very happy in a less populated world.