Although I presume if you nominate your keeper, he can still stay on the pitch as he's quite clearly still involved in the penalty shoot out? Or is there some daft rule that you can't nominate him?
No, you can nominate your keeper not to take one, but yes he does get to stay on the pitch. The minimum requirement is 7 players, one of which must be a keeper. If you get 4 players sent off the match is abandoned. Something that was attempted by one team who had 3 off who deliberately attempted to get a 4th player sent off thinking it would force a re-match (it didn't).