Welcome to the forum,
you do NOT have a water pump - and you a good ol fashion dynamometer, which is an old school alternator.
This engine moves the water around via a thermosyphon system - hot water is less dense, thus rises once cooled drops back down via the radiator. Very very simple device - BUT you must keep that radiator REAL clean.
Now lets talk about the lack of charging - that dyno produces AC - it should have 2 leads (maybe 3) and if you can find the leads you can hook a volt meter to them and with engine running near WOT and you should see 30+ volts AC. The rectifier may be at fault, turning the AC to DC.
Most dynos never go bad - the bearings DO go bad, but the making the juice rarely goes bad.
The dyno has 6 nuts - 5 of them are easy to get off - 1 of them is "hard" to get off and a real PITA tp get back on.
Get a 10 mm ratcheting wrench - something like 2 degree clicks.
What I came up with was to drill a very small hole RIGHT in the middle of the lower middle bolt. I am talking like 1/32 or so - then I get the body back on and you can place the 5 easy nuts on and get them snug - then there is enough room to take a piece of stiff wire and place it INTO the hole at the end of the bolt, allow the wire to come out past, then slide the nut down the wire and your finger can give it a few flicks and it will spin right on. Trust me any other way makes you want to pull your hair out!