I am guessing that the side “wings” of the bed platform fold down flat against the sides of the shopping cart (cart) Inside the canopy it would be wise to have the flat “bed” platform be in three separate sections to allow the sides to fold and the center section be a two-piece wood platform whose pieces can slide to the side to assist entering the unit. Enter your mobile bedroom then slide the rear section to its proper place allowing you to lay down while on your side then slide the front half of the center platform to its position and you are ready for full-length full-width dozing ecstasy.
There is open-air storage at the cart bottom. Weight there would assist stability. Theft is a constant problem. Maybe a sturdy container of some type that can be chained and locked to the cart. Scumballs abound. Will one or more of them tip the cart over or roll you away while sleeping? If there are other homeless in an encampment maybe there will be safety in numbers.
A crafty person may be able to create outriggers that can be folded outward to provide stability. A locking mechanism to prevent hooligans from folding the outriggers in then tipping your house over would be handy.
If a cart from a closed-down store is found that may keep the cops from messing with you. If possible remove all store markings that indicate the entity that originally owned the cart.
Staying dry is critical. The “windows” need some device that securely seals from the inside that repels the water. Maybe waterproof material can cover the opening and extend to the sleeping platform edge so that water entering flows down then exits at the platform edge then drips upon the ground. The door located above the handy step also needs to be waterproof. It can have a sliding portion akin to many house windows that when open allows ventilation but when closed is a barrier to rain. Where the door meets the sleeping platform and above needs sealing around the edges where it meets the canvas. Stores such as Lowes and Home Depot have a lot of stuff that can be used to create a water barrier. The crafty creative crowd will surely find the solution to water tightness. The fending off water will also allow hiding from cold winter winds. The cold creeps in but at least those deadly frigid winds can be kept away while you snuggle within that comfy quality sleeping bag.
When summer heat hits ventilation is critical. Those “windows” reduce privacy but sacrifices must be made at times. Sleeping away from the normal flow of non-homeless life allows less worry about hiding from humanity.
The normal cargo carrying location of the cart is open to the elements in the view above. I wonder if waterproof material can line the area to keep water out. Security of property is always critical. Maybe a lockable container can be bolted to the cart then use caulk or another sealant where the bolts penetrate the waterproof material. Lots of possibilities.
Another possibility is to build your own cart!!! I would use larger wheels and the sleeping platform would be closer to the ground to lower the center of gravity. Try to craft the craft to allow standing fully upright. The sleeping platform could be lengthwise to avoid the need for a folding platform. I saw some ideas for these on the Web so will create a new post showing them.