R vs. P+P+P

With absolute perfect play I think you can, but us very difficult, also depends on exact position so I don't know about this one.

If I was White in this position and Black offered a draw, I'd accept. But I would probably be wrong, lol

In this position, white has a forced mate in 27. Practically speaking, I might settle for a draw.
(Don't believe someone like me could calculate that? I can't.... but Shredder can!)
http://www.shredderchess.com/online-chess/online-databases/endgame-database.html