Cooking with gas is the most common and having a side door, window or sky light open while cooking is recommended. You could consider using a camping stove using small canisters then you only need to attach the gas to the stove when you need it. This would be a more costly approach but at least you would have more control and you can move the camping stove outside.
A larger gas bottle would require a hole in the floor near the bottle to allow any escaping gas to flow out of the van and a gas bottle could also be attached/detached as and when you need it.
A carbon monoxide alarm should also be fitted.
For hot/warm water how about a plastic water container which you paint black, You place this outside in the sun and a few hours later you have hot water. Another take on this is a black waste pipe on the roof, similar to what plumber use to carry pipe, but you use black pvc drain pipe. At one end you fit a tap to draw off water and at the other end a screw fitted cap. Fill pipe with water and this heats up from the sun as you drive, Both these methods will provide some hot water but only a gallon or two.
Maybe buy some large thermos flasks which you can fill with water you have boiled in a kettle. this will provide some very hot water during the day for washing. I would forget about showers and go for a damp sponge and wet wipes, sort of bed bath but without the bed or the nurse. Wet wipes can be bought cheaply from Home Bargins in the baby section and are fragrant free.
The fridge issue might mean thinking outside the box, or to be precise, outside the coolbox. What food stuff are you planning to keep that requires a fridge? You might have to shop daily or every 2 days and buy products that don't need to be kept cold.
These are all challenges that you need to resolved by thinking beyond the norm.
