He probably brought his own laptop (I always did on the deployments I went on) and he probably had access to commercial internet access depending on where he was.
Yep, that's correct: I had my own laptop and commercial internet access through most of the deployment.
unlikely -- the websites he would have needed to use to build it are usually blocked!
On the civilian side I was once almost driven to tears trying to get someone to unblock StackOverflow because it was a "social" site, though I found most of the whitelisting guys to be much more reasonable.
He explains, in the article, checking this with the person he replaced before he went on his deployment. He specifically mentions GitHub and Heroku.