Actually, game saves are also linked to each account and can't be transferred for use on another account. No other gamertag can access a save made by another gamertag.
Yes they can.
Not all games allow it but you can move saves between profile by signing into the profile you want to move it to then find the save and select move. doing this will transfer ownership of the save to the new profile.
Like I said not all games allow it.
Oblivion is one game that lets you move saves between profiles. Alien vs predator doesn't allow it.
I've just tested it my self. I was able to transfer an oblivion save to one of my spare profiles and was able to load the save.