Ammeter to Voltmeter...who does it?

Yes, there a few different ways things can be arranged.
I don't know why the arrangement you currently have uses a fuse between the two batteries. There might be a reason a fast opening device was preferred.

I don't know either...my first thought was maybe it's there, in case the something happens to the solenoid, like the 12V power source spikes. I really have no idea.

The voltmeter as drawn will be on full time. Probably better to have a voltmeter wired to turn on with key in Run and accessory. no?

As it stands in stock form now, the ammeter is on full time...will it hurt the voltmeter, if it stays on full time? If so, I can find a switched 12V source under the dash and use it to power the voltmeter.

Is it possible to have a device that regulates the charging rate of the coach battery?

Yes, it is. It requires the removal of the existing Coach/House battery charging solenoid and replacing it with an updated charging system. It's on the list of things to do.

One advantage of an ammeter is that is shows charging, how much and when its done. The voltmeter only shows whether the alternator is producing enough power it can potentially charge the battery(s).
If the status of the second battery is important, might be worth having a second ammeter and/or voltmeter for that system. Obviously if you did an ammeter for it, it would be best with an external shunt. The ones for marine and aircraft will probably be the best, and most expensive, as they probably must meet instrumentation certifications for those uses. But those would be a couple of places to search for info and general availability.

The Coach/House battery has a second ammeter, located at the Power Distribution Center under the kitchen counter. When you press the switch, it gives you the health of the battery, and whether it's charging or not.