More modern motherboards (socket 7, most socket 5, late socket 3) support both.
If you insert an EDO in a mobo that only supports FPM, it just won't boot. They both work at the same voltage, so nothing will be damaged.

I have a montherboard that supports both in the same socket. So you're good to go.

does it support both at the same time? My mobo has 8mb of onboad ram.

I don't know (I doubt it). Check the motherboard manual to be 100% sure.

No, if inserted both types on a machine that supports both, they'll run as FPM.

This motherboard doesn't technically have manual. Never did. The closest manual i can find just says it has an available slot for ram.

https://files.support.epson.com/pdf/an910c/an910cpg.pdf