He said he shuts the machine down on nights and weekends. I am not familiar with EC2, but doesn't that mean that the desktop isn't persistent from day to day? Yes, he can connect and disconnect at will throughout the day while it stays the same, but shutting down the machine at night shuts down all the apps he had open I assume. Am I wrong?

No differently than if you shut your computer down and boot it up again, if he's configured it accordingly with an elastic block store for the filesystem, etc.

Not if you shut down with "hibernate".

With no risk of hardware failure.

Well, minimal. http://www.google.com/search?q=amazon+ec2+down

I have that too. It costs me nothing (my electricity is comped currently), it's a faster machine and I have physical control of it if necessary.

What do you do when it breaks? Who pays for the bandwdith? How much do you have? What if your house burns down?