We have an R-21EC that we use out of Cape May, NJ, in the ocean and lower Delaware Bay. Here are my thoughts, based on some -- but not vast -- experience in waves of the size you mention. (For calibration, I believe the waves I describe are 4-5 feet, but I have come back to the dock to have other folks tell me they were 6-8 feet; I stand by my estimates, but they are just estimates.) In general, I am very impressed by the seaworthiness and handling of the R-21EC.
If you are heading straight into sufficiently short, steep 4-foot waves, you will probably stick the bow under some of them (depends on your speed, the length of the waves, steepness, etc.). This is not life-threatening, but it gets your attention. In my experience, the forward deck drains quickly and not much water gets into the cockpit. These conditions can be fun for a while, but, speaking for myself, I wouldn't want to do it for a long time. There is a LOT of boat motion.
If you are running with these waves, the boat is dry and should not broach, but you must be vigorous with the wheel.
If you cannot avoid running across these waves, I would think you would be very unhappy. There will be much uncomfortable rolling, but even larger boats would likely be uncomfortable. Some waves will likely break into the cockpit, depending on exact wave shape, which brings me to your next question...
I have had solid water roll into the cockpit, but not a lot. If it happens more than once, I take it as a message to change course enough to stop it. In my limited experience, the bilge pump has managed just fine. I don't know what would happen if a course change was not an option. In my experience, the boat has never rolled down so far that water pours over the side -- my cockpit water has come from individual waves.
I don't have air conditioning, so I defer to others. I believe that air conditioning runs on 110V, 60Hz. The diesel normally charges a 12V battery. I rather doubt that any practical (for an R-21) battery/inverter combination would be adequate to run air conditioning.