Their new record is streaming on Absolute Punk, so you've got some listening to do, given you enjoy the album you picked up. They're really good, this new one is easily my favorite pop rock album for this summer.
I'm liking Safe Upon the Shore. Not my favourite album, but it's quite a bit like what I think Fortune's Favour was trying to be.
As for Lullabies for Bloodshot Eyes, I have it, and enjoy it. It's in quite a few ways similar to his GBS stuff, actually, but it's different enough that you should prolly give it a listen before buying.
Yes, musicians are allowed to enter. It doesn't have to be an original song but if you want to go ahead. For the non-original songs it depends! If its fine to have a remix/arrangement of a song, as long as its obviously a remix. If its a cover performance, then no it wouldn't be allowed.