Nope, you can't play a ps3 guitar in a ps2, but if your ps2 guitar gets inserted in the USB port then you can play it on your ps3.
Yes!
have a look at the compatability matrix with the link below
Yes
you can use it for the bass, guitar, and drums, just not the microphone
the ps2 kramer (GH3) and the guitar hero 1&2 guitars work for ps2 rock band games
yes
yes
yes
Rock Band games on PS2 only support PS2-style guitars and PS2/3 Rock Band guitars and drum kits. Guitar Hero: Aerosmith and newer on PS2 support all instruments from all consoles that the games have note charts for (so no drums on GH:Aerosmith but 360 and PS3 drums work on all full-band GH games).
Yes you can I do it all the time for my ps2
yes it will guitar hero controllers work on rock band