I would say yes to the first part. There's nothing in the Roughrider section that says he actually has to own the mount. All he has to do is spend 1 hour training with the mount. But don't forget that the player whose pet you try to use as a mount maybe wants to ride his pet himself ;)
The part concerning wildshaped or otherwise polymorphed PCs is a little bit more tricky. I suppose it depends on the GM.
Also, the roughrider will still have to spend 1 hour training with the other PC.
I suppose if such a situation would come up at my table, I'd say it works if the player of the "mount" PC is ok with being used as a mount (If he isn't ok with it, he wouldn't agree to spend 1 hour training with the roughrider anyway). Since the main purpose of the game is to create a fun time for everyone, I don't see any reason to forbid something everybody seems to be enjoying and that's not clearly contradicted by the rules.