Hey, I'm not yet an escape room owner but I'm in the process of opening one in my city (Quito, Ecuador). So here are my recommendations:
City Permits: This depends on where you live, here it's really simple. We had an inspection from the fire department to check we had the necessary emergency exits and such. No more permits are needed in my city.
Legal and physical aspects: That one was easy for us too, since our team had a lawyer, an architect and a civil engineer. Our lawyer registered the business, made the contract for renting the property and made sure we were doing everything right. The rest of the team (architect and civil engineer) measured the property, drew some CADs of it and a 3D model in Sketchup, that was really helpful since it's easier to move things around in a computer than physically there, so when we had the 3D model, we actually changed some of the rooms' design to make it more enjoyable.
We hired a contractor to install a few gypsum boards and nothing else, the painting and decorations was entirely on us, which made everything cheaper.
I'm sure you're going to need an electrician if you don't have the necessary knowledge, it's not much that usually needs to be done (lighting and magnetic door locks) but it's easy to screw it up.
You also need to keep in mind that if your design includes some sort of automation, you're going to need someone to implement it. If you feel like doing this yourself, I would recommend getting an Arduino kit and playing with it.
Good luck!