What Mike said.
Also:
#2 When the switch is OFF and plugged into shore power the converter supplies 12 volt power. In most cases this is NOT a normal condition, the battery disconnect should be connected when plugged in so that the batteries stay charged up. This was more important in the old days as older model converters needed the battery to buffer the power they were producing. This is rarely the case with modern chargers, but there is still no reason to disconnect the battery when plugged in. (Except if you are concerned about overcharging the batteries)
As Mike states you should verify the converter / charger installed. Most chargers today will treat your battery OK. At least much better than the older models. If you have the Parallax model there is a temperature module that can be added that allows a somewhat better charging cycle.
https://www.amazon.com/Parallax-Power-4400TAU-Temperature-Compensation/dp/B00MI3UY8K But verify your charger to make sure it is compatible.
The only time the battery disconnect switch should be disconnected is when putting the coach in long term storage with no available shore power. And keep in mind that even with the switch disconnected there is still some draw as the LP and CO detectors are often wired around the disconnect. That, along with normal self-discharge can drain your battery completely in a month or so. Many people use a solar trickle charger to maintain the batteries when in storage, or remove them from the coach and keep them in a garage on a trickle charger.
#3 Yes. And you should never drain the battery more than 50%. Many recommend not going below 75% of full charge. It can be hard to tell that without a battery monitor but there are charts that relate charge to voltage. But it is important to remember that full charge is 12.7 volts and 50% charge is 12.0 volts. Never, ever allow your batteries to go below 12 volts. You can get simple plug in meters that will show the charge if you do not have a real monitor.
cheap 12v meter