I've got a Canon FD 300/4 L that's waiting for me to get a suitable mirrorless body.
Do you get the full focal range out of them on mirroless then? the main thing stopping convertor plates being a viable product (though some are out there) for EF bodies was you lost (IIRC) infinity.
Yes, you do.
Mirrorless cameras don't need to leave space for a flapping mirror between the lens and image plane, so the lens mount is quite a bit closer to the image plane, leaving a fair amount of space left for the adapter whilst still putting the lens the correct distance from the sensor.
Canon FD has a lens mount to film plane distance of 42 mm
Canon EF-M has a lens mount to sensor plane distance of 18 mm, which means your adapter has to be 24 mm between its two mounts
Canon EF/EF-S is a lens to sensor distance of 44 mm, meaning an FD lens to EF adaptor would have to mount the lens 2 mm inside the camera body in order to retain infinity focus, which obviously isn't going to happen. Even a thin adapter would work like a ~5 mm extension tube.
Apparently it was possible to change the mount on some lenses from FD to EF. At the time, Canon produced a mount converter which retained infinity focus, but acted as a ~1.2x teleconverter. I'm led to believe they almost all went to pros with big expensive lenses, and are now like hen's teeth. You can get 3rd party versions still, but since they don't cost more than the straight tube adapters, I can't imagine the effect on the lens image quality is good.
A bit of a google shows FD adapters for EF-M, RF, Sony NEX, Fuji X, μ4/3, Nikon Z, Leica L, mostly around £25 - £30
FD lenses are fully mechanical, so there isn't auto-anything from the camera end. Manual focus, manual or aperture priority metering/exposure, and quite probably manual pre-exposure stop down