Once again, you are talking about a rental in Iceland, European motorhome technology, most responses you get here will be about how things work in North America.
How long you can go on battery power will depend on use. Much of European RVing is dry camping, no water, power, sewer hookups, so systems are designed to minimize use of electrical power, and you rebuild that running the engine if you don't have a plug in.
The RV you rent will not have a permanent LPG tank. Bottled gas is handled as removable bottles (different from our BBQ tanks but same idea) and usually on a tank exchange basis. Refrigerator, cooking, heating, and heating water will use gas. Refrigeration uses little gas. Cooking and heating water uses moderate amounts of gas, a 10 Kg tank might last a couple weeks. Heating can use huge amounts of gas, as much as a tank a day if temperatures are near freezing and you try to keep the RV warm enough for living in your underwear. Depending on size, heating might be forced air (uses battery power) or might be convection or radiant (uses LPG only).
For charging phones, the standard is a USB adaptor from a 12V outlet, or if you have mains power, a 240V to USB power supply off the mains outlet. USB power supplies for mains are readily available in Europe, I was able to replace all the stuff I left in the seat pocket of the plane at CDG with pieces from a phone store in the mall at Ploesti.
"Other stuff" scares me. Tablets are generally USB power, but higher ratings, 1-2 amps rather than the 500 milliamp rating in the USB standard. Many of our 12v adaptors can handle the extra current a tablet wants, you have to pay attention when you buy. I buy Apple USB chargers to stay safe on my Apple devices, have an international kit that covers almost any outlet I find, 100-250V, 50-60 cycle AC.
Laptop computers are more of a problem, most need more than 12V for charging, thus special converter/inverter power supplies for 12V sources going up to 14-20V for the computer. On the other hand, every laptop AC power supply I've had in the past 10 years has been "universal" i.e. 100-250V, 50-60 cycle or broader. You just need the adapter for the plug. I suspect Iceland (will be 240V, 50 cycle) uses the DIN two prong plug widely used in Western Europe.
This is a tricky place for asking these questions, many people are not catching on to the fact that you are renting a Euro RV in Iceland, with different systems than are used in North America, and are giving answers that might be more useful if you were renting in Las Vegas to tour the SW United States.
Your YouTube link takes me to an array of about 40 different places, none looking relevant.
