The scheme in the
draft BIP won't work because Alice only signs the first input of Bob.Payout, Bob is free to change the second input in order to not reveal x.
Signatures apply to the entire transaction. There are options to only sign part of the transaction, but by default all outputs are signed.
No they don't, signatures apply to the whole transaction but with the other inputs set to 0 see
https://en.bitcoin.it/wiki/OP_CHECKSIGAs mentioned in another thread, transaction signing is weird, complicated and needs updating.