Only the launch consoles have PS2 support, but every single PS3, even the slims can play orginal PS1 games from original discs.
This is what has annoyed so many people, why give a 3rd gen console 1st gen support then remove 2nd gen support?! They put it down to cost cutting, every phat PS3 they sold, $ony were losing money (even with the inferior EU models). But it was also clear that they still wanted to sell PS2 consoles, seeing that even today new games are still being ported to PS2.
But now bringing back PS2 support of PSN only games, really does show the green dollar signs in from of every $ony official.
By "ps1 ps3" games do you mean the downloadable games which were hacked by duplex? I think those will run from hdd. If you mean original ps1 discs, then just use your pc. Copy game to pc as bin file, then burn it onto a cd.