He was filing fake tax returns. That probably exposed his IP in logs on government servers.
The safe bet is that every site that you access logs your IP address. At the very least.
What on earth? Isn't using a VPN the bare minimum when you're doing something potentially illegal?
Maybe he did. Unless he's careful in picking his VPN provider they probably have some level of cooperation with the FBI.
He didn't, but getting anonymous access to a VPN wasn't exactly the simplest thing then. And if you think they would be unable to find the precise location of the aircard, it's not really adding any protection.