I've lived out of my Ford Explorer for months at a time over the past six years.
Sleeping? Up until now I've used a "half-twin" memory foam mattress topper placed on top of the folded-down seats. Basically, a 2" topper cut in half lengthwise and stacked. As a side sleeper, I don't need a wide bed. This arrangement leaves plenty of room for storage, both in the seatwells and alongside the bed. Entry is from the driver's seat, over the center console.
Bathroom? Pooping inside a vehicle is [censored] disgusting! Unless you have a bowel disorder, you should be able to schedule your movements...for instance, if you go after breakfast, then cook breakfast near a public bathroom. When out in the boonies, a cathole works fine.
Shower? Public recreation centers are my favorite option...a day pass gets you a workout and a shower at most of them. Baby wipes will do in a pinch. Sneaking cheap or even free showers at campgrounds is a fun possibility. In warm weather, bathing in a creek is perfect. A solar shower bag is useful if you spent a lot of time boondocking. Let's face it; if going a couple days without a shower is unthinkable, the car life ain't for you!
Cooking? Propane stove in the passenger seat. Wait, what? Yes, it's perfectly safe, as long as you use common sense. 1) Place the stove on a level board. 2) Always open at least one window for ventilation. 3) Never, EVER leave food cooking unattended. 4) Close the valve tightly after use. 5) Let the stove cool before putting it away. 6) Have a small fire extinguisher on hand, just in case. I've cooked thousands of meals in my truck on a $20 campstove with no issues whatsoever. It's perfectly OK to leave the stove hooked up to the canister; however, after it has been connected for a prolonged period of time, don't disconnect it until it is empty!
Food storage? Humans lived for millennia without refrigerators. Many foods keep surprisingly well at ambient temperature, especially in cooler weather. Broccoli will last a few days before flowering. Cheeses (except cream cheese) will hold out for a couple days or more. Unopened butter is good below 85 F for upwards of a week. Apples and citrus handle room temperature well. Fresh asparagus will last a few days; if it's already slimy, you'd better eat it right away. Salad greens wilt within 24 hours, so eat them quickly. Farm fresh eggs are fine at room temperature. Jar alfredo sauce can last 24 hours opened, but heat the second half good just in case. Buy avocados at varying states of ripeness, in order to have one ready every day. Raw meat at ambient temperature is highly unsanitary; time to go vegetarian!
Water storage? Plastic gallon jugs are my favorite. A flip-top water bottle works great for both drinking and washing hands. Depending on your habits, you may need anywhere from two to seven jugs. Keep one full and unopened in storage for emergencies.
Dishwashing? Throw away your plastic dishes and utensils. Trying to clean grease off plastic (including so-called "nonstick" surfaces) is a nightmare. By contrast, even the coldest soapy water will leave a steel or aluminum surface squeaky clean. Wipe excess grease out with a paper towel (or a slice of bread) before washing. There is no need to wash the outside / bottom of your pot!