Hope you do not plan on putting a whole lot of weight on that.
It really could use a face frame or a soild back to stiffen it up.
Those tiny wheels are going to be a pain to roll it around on.
Yes a piano hindge would be great.
Here's some folding leg brackets.
Going to need at least two of them.
A slab of plywood as a shelf is likly to warp unless you build a frame of some kind under it.