Indeed, I can imagine trying to build an AVRcam on a breadboard could be a daunting task...I wish you luck
On to the questions...
The OV6620 is responsible for providing the clock source for the mega8. The OV6620 will output its clock signal (at 17.7 MHz) on one of its output lines, but it doesn't do this by default. This is where the tiny12 comes in. Its sole purpose in life is to send an I2C command to the OV6620 at power-up so that the OV6620 will output its 17.7 MHz clock signal for use by the mega8. The UART timing on the mega8 depends upon this signal being present.
Yes, the only fuse that should be asserted is the CKOPT fuse (indicating an external, rail-to-rail clock signal will be provided, i.e., the signal I mentioned above). All the remaining fuses are not asserted. I usually do the fuse programming with PonyProg; in PonyProg terms, the only fuse with a check-mark is the CKOPT fuse.
The fuse settings for the tiny12 are the factory default (I don't recall what they all are, but simply leave them as is). I don't see why a tiny13 couldn't be made to work, though I haven't played with the tiny13s. It may just take some minor code tweaks.