Referring to the water heater, you must be sure it is full of water before you turn on the electric heating element. If the tank is empty, the electric heater will burn out in seconds. If the heating element is turned on, it will come on as soon as you plug in the shore line and there goes your element.
Since this is new to you, I suggest that before you connect the shore line or start the generator, remove the water heater cover on the outside and confirm that the electric element is turned off. There's a small black switch on the lower left that is partially hidden by the gas plumbing. After seeing that it is off, and with water pressure (by city water hookup or water pump turned on) lift the safety valve to confirm that the water heater tank is full. Also open the hot water on the kitchen sink. Then it's okay to turn on the electric heating element.
Yes, you can have both the electric element and the propane burner turned on at the same time for faster water heating. It could take nearly an hour to heat the water with electricity only if the water is really cold, like 40 degrees. 30 to 45 minutes is more likely. The propane would do it in about half that time and the two combined would be 20 minutes or less. You decide if you need it quickly or if you need to conserve your propane. I'm doing this mentally so I may be wrong but I think it would take about 1/4 pound of propane to heat one tank. Remember that if you leave the propane burner on, it will kick on periodically to keep the water hot. You can conserve propane by turning it off as soon as you have enough hot water each time you need it and let the electric element keep it warm.
As for the stove, I don't know for sure, but I don't see why it wouldn't work with the slide in. You need to turn on the exhaust hood with the slide in or out.
PS Run your furnace for at least 5 minutes with the door open before you take it anywhere. The first use will burn off oil that's on the furnace from manufacturing, which will set off your smoke alarm. We first used it before 6 AM during our first trip. That didn't make us new friends in the campground!
Have fun and post on this forum with any questions. There are lots of experienced RVer's participating. I've learned a lot here. And some the hard way (see above).