PS3 does not have backwards compatibility with the PS2 - the original 60 gig "fat" models do, but they can be hard to find since those early units were susceptible to the Yellow Light death. There are some PS2 games that have been emulated and can be downloaded through the PSN store, but the selection is limited.
PS1 is compatible with PS3 though - almost every game works.
As for PS4 requiring a fee to play online, so what? It's only $50, and it's PS+. You'll not only get to game online, but you'll still get tons of free games and huge discounts - it pays for itself in no time at all. It's not a rip job like XBL![]()