For many reasons some of which are provided in the related question
No you can not play the PS2 games on the new PS3 and you can not play the PS3 games on the PS2
No.But PS3 can play PS2 games and PS2 can play PS1 games.
PS3 can play PS2 games.
The PS2 can never play PS3 games
every ps3 you can play ps2 games on
It all depends what kind of ps3 you have. If you have an older 60 GB then yes you can play ps2 games on your ps3, but these ps3's are not being manufactured anymore. So if you bought your ps3 right when they came out and it's a 60 GB, chances are you can play ps2 games in your ps3, but if you more recently bought your ps3, then most likely it wont play ps2 games.
No PS3 can Play all PS2 games
Yes (both PS1 and PS2) if you have the 60gb version. The 40 wont. Please note you can play PS1 games through your PS3, on your PSP (remote play) but not yet PS2 games.
It is possible to play PS2 games on a PS3 game system. You cannot play PS3 games on a PS2.
You can not play PS3 games on a PS2 console
No, but some versions of the ps3 can play ps2 games
No. Since the ps3 is much more advanced then ps2, it wont be able to play it. Think of it like this. If you look at ps1, you cant play ps2 games there because ps2 games are too advanced to be played from ps1. Same applies for ps3 to ps2