Sadly not. There have been talks of PS2 emulation coming soon, but we might have to wait until the PS2 stops being manufactured. There's a date floating around somewhere, but I can't think of it off the top of my head.
Nope. Which sucks since the PS2 has some of the best games around. They can however play PS1 games. There is an older version of the PS3 that plays PS2 games but they're extremely hard (if not impossible) to find now.