The order would come from the private security companies, they would only enforce order for the people who hired them though. See, it wouldn't be just one faction imposing order, it wouldn't even be two or three, but a dozen, a hundred, a thousand maybe. And thats why it would be different. First of all, you could just choose not to have one, and take your chances on your own. You couldn't go rioting, because then you would have to deal with all the security companies of the people you pissed off, but if you were very confident in your ability to defend yourself, you could do so. And if the security company you subscribe to begins to not be one you want to deal with anymore, you are free to switch to another. So that means they have to keep you happy to keep your business (where as governments merely need to control the land you are on).
Admittedly there would be FAR fewer "laws" (actually officially there would be none, but there would definitely be things which if you did would have a similar penalty)
The security companies would primarily just be that, security. They would only look after you specifically, not society. So no, there wouldn;t be anyone enforcing speeding laws, or drug laws, or age limits (actually speeding might have the road building company having its own security deal with that)
They would deal with things like: Theft, murder, assault, rape, contract breaking, trespassing, kidnapping, ect ect.
Technology... I think you've got it backwards. Most technological advancements are made by people trying to make a profit, or else by the military and reverse engineered to make a profit. There would be more businesses then ever to take care of the first, and the weapons companies would take care of the latter. In fact, its possible that some companies free from taxes, would pop up specifically To invent things and sell them to other companies to use.
As for the military... well mostly that would be up to the militia. there's some debate about how that would be funded but usually the consensus is funded by the members who would do it as a part time job- not full time. They would organize themselves into small coalitions. And then those coalitions would form themselves into larger ones and so on and so on, where each member of the militias vote on representatives to send to the step higher, so what you've got is a bottom up military. It would purely be defensive though, as offense is much more expensive and they wont be able to afford to be the aggressor.
As for it lasting... what will who do? the only ones physically capable of a forceful takeover would be the security companies, who would have to deal with both eachother and the militias, or else the militias, who will have to deal with both eachother, and the security companies.
Your right though, it couldn;t form in any modern society, because no society is ready to dissolve their government by their own accord. I think if it formed, it would last. Actually I think it would possibly be the most stable government possible, because there would be no positions for corrupt people to try and get.