So if riseup.net had been hosted on, say, EC2, what would the FBI have seized? The server hosting the VM and many other completely unrelated VMs? Scary thought.
Also, if you haven't done so already I encourage you to read the FAQ at the end of the page. It has one of the best answers to "Doesn’t Mixmaster/anonymous remailers enable criminals to do bad things?" I've ever seen.
If previous seizures are any indication yes. They identify machines by IP and even if its a virtual machine they seize the server running it.
Can't comment on whether or not its effective, and of course if you have a disaster recovery plan and your site pops back up I don't know what they do, I guess they play whack-a-mole with search warrants.
Wait, seizing server running VM makes zero sense - VM can be run on different physical servers at different moments and freely migrated. What would they be seizing actually - silicon and metal in hope it somehow would given them a clue about something that happened eons (in CPU time) ago on the same hardware? That's like arresting a person because he was breathing the same air as a criminal did.
Even if Amazon does not actually migrate VMs I'm sure some other cloud providers do.
OTOH they could seize storage media where the images are stored. That would be a major catastrophe for any cloud provider.