It’s not very practical to cook, heat, or cool with battery power. Creating heat and cooling (removing heat) require a huge amount of battery power and a very large means for charging. It’s very hard to have enough solar panels and batteries on a van to run an air conditioner, and then adding an electric cooker and other power-hungry appliances would likely push it well into the impossible.
For creating heat use fossil fuel like propane, for air conditioning use a generator or be plugged into shore power.
If you plan to spend the hotter months in areas with very low humidity (where it’s not too hot) you may be able to get away with an evaporative cooler (swamp cooler) on battery power. Key here is low humidity - evaporative coolers don’t work well where it’s humid unless you use some kind of indirect type. Van Dweller has stated that he uses an indirect evap cooler. I have no experience with indirect evap coolers.
A practical size solar/battery system will run LED lights, device charging, fans, entertainment, etc.