Has anyone thought that maybe Snape could have told Dumledore about his suspisions of Quirrel and as such Dumbledore told Snape to keep an eye on Quirrel.

Afterall, Dumbledore has reason to trust Snape so why not use him as a "protector-aid" for the stone.

Also, all the books are written from the view of Harry, so when Dumbledore & Snape have discussions Harry won't know what they're talking about cos he isn't there.

Very good question. Never really thought about it until now.