Partial answers
1. They state that they are impervious to subpoenas because they can not associate a name and box number. The government/court/whatever could trace you by the retinal scan. No?
How could the government get your retinal scan to match it?
2. They do not talk about insurance for fire or theft. Are they insured? Can they be insured? How can you prove what you had in their possession in the event of either?
I don't know. The boxes are "fire-resistant" like bank safety deposit boxes. If a bank box burned to the ground or exploded, etc., I don't know how you'd prove how much cash you had in your box either. It's a good question.
3. Other than tracking them down with Guido and a pipe wrench, what is to keep them from running off with the contents?
I suppose only the criminal statutes. This place has been in business for several years. I remember reading an article about the owner, who has a good background. If I find the article, I'll link to it. I suppose this business relationship is no different than trusting anything to a presumably honest business. When you bring your car in for service, there's a chance the repair facility might go out of business that day and steal your car.
