Do you have a digital timer ? iPhone ?
If so, use the timer to fill a one gal water bottle (note the position of the spigot to determine flow rate).
Next, with the water spigot turned on in the same position, fill your water tank in the rv using the timer. When its full take note on how long it took. You'll see it start to overflow when full.
EX: if it took 10 secs to fill the one gal jug and it took 100 secs to fill your water tank, you have 10 gals in the tank.
Water heater: 6 gal water heater tank is probably what it has . Learn the procedure to purge the air from it so your faucets don't spit.
Re: black and gray tanks capacities. It a short amt of time , while using the rig, you will be able to guesstimate how many gals your holding tank are as long as you have a good idea of how many gals your holding and using in the freshwater tank.
I would go to a place with a dump station and clean those tanks using a wand or tank sprayer.
Once you do that, place a 5 gal bucket to catch water from the open gray dump valve. I would run each faucet one at a time , from the bathroom sink and then the kitchen sink to be sure both drain into the gray tank. Sometimes rv's are plumbed to drain gray bathroom sink water into the BLACK tank causing it to fill faster than you would expect. It's just nice to know how your system is set up regardless of tank sizes. It makes it easier to guesstimate your amounts as you use it .
RE the genny: With the age of your rig, I would suspect the wires have corrosion or have broken off somewhere that's possibly exposed to the elements is where I would start looking. Check your grounds .