"now I need some software to backup C64 diskettes, Amiga can do it, right?"
I may be wrong but I think that you need either a A64 dongle or Easy 1541 cable to hook up a 1541 or 1571 Commodore drive to your Amiga to get it to read C64 disks.
I'm using my A64 with at 1571 to backup all of my old C64 5.25" floppies right now... slow going but it works!