Hot Water Pressure

Many water heaters have a check valve on the outlet, this will in fact slightly reduce pressure (you should NOT notice) but as they age minerals build up to the point where they may totaly fail to open,, In which case you are NOT going to be in hot water till you do something about it.

The one on the hot water outlet is needed if you have a single valve bypass system.. BUT.. You can replace with a quarter turn valve if you like and kiss check valve issues goodby (Provided you remember the valve spring and fall)

The one that may be on the cold water INLET.. I am still trying to figure out why they put em there..

If the pressure switch on your water pump is adjusted properly, the pump won't pulsate as much.
My three new trailers all needed to be adjusted and afterwards, the pumps didn't pusate on lower flow.

I think so. Hot water may be set that way to conserve hot water as hw supply is limited (6 Gallons ?). As a result the pump can pump more water per minute that will flow through the hw system and thus cycle off. Quite normal.

If this is a separate hot & cold faucets, it's probably a clogged aerator screen.

NO! that is not normal. You have some kind of restriction on the hot water line.