This page discusses these points.
Generally this is no problem to the controller, however it may not be good for the batteries.
A generator will tend to keep the batteries fully charged. So the controller, when it goes into regenerative braking, has to dump the braking energy into already fully charged batteries! It can do this - but only by overcharging the batteries, which may not do them any good.
Be aware of the overvoltage level of the controller. If the overcharged battery voltage hits this, regenerative braking will cease - which may be dangerous.
Generally the over voltage level is 47v for 12v, 24v and 36v controllers and 68v for 48v versions. Overcharging the batteries is therefore unlikely to hit the limit, except on 36v versions. If this is likely to be a problem, consider using a 48v controller.
Instead of the generator keeping the batteries fully charged, it should be adjusted to keep them perhaps 80% charged, so there is adequate spare for regenerative braking. However, keeping a lead acid battery in a partly discharged state may not be good for it.
Sorry, no. Batteries are essentially capacitive and work well with pwm chopped currents. However a generator is essentially an inductive source, so chopping its output at 20kHz will generate huge voltage spikes - although these are unlikely to damage the controller, it will not work properly and the generator's electronics are not designed to supply this sort of current.
Sorry, 4QD cannot advise on batteries. We do not manufacture vehicles, so do not source batteries except rarely for test purposes, so we have little practical experience.
Our experience with generators is also effectively zero.