" I cant write anything to the fat32 disk for some reason."
knoppix mounts everything as read only.
"I played around with the permissions, but that didnt change anything"
You have to umount the partition and the mount it as read/write (read/write is the default).
"I know the what the name means, Wine Is Not an Emulator, please explain in simple terms if you can."
"Wine Is Not an Emulator" is splitting hairs. You can emulate both software and hardware. For example if you were running an Intel 586 computer and using an emulator for DEC PDP 11 then the emulator has to emulate both the DEC hardware and software. WINE runs on Linux/i586 and emulates Windows running on an i586. Therefore WINE can get by with only emulating the Windows software and not have to emulate the i586 hardware.
Be prepared. Create a LifeBoat CD.