I've heard that with App Outlaws, yes a 2nd season will be made. With a full 12-16 episodes. I can't say regarding the other shows. As far as permits/laws, I'm sure History Channel would rather do as they please and pay the fine, than try to operate within the law and make less entertaining television. They probably have a team of lawyers 100 strong to help them through any situation that may arise.
That being said, I have my suspicion that a lot of the footage of the AO diggers was all filmed in 1 day, all on the same ground, with permission from the land owner. All had the same clothes on for every episode, a dead leaf stuck to the back of a shirt was there on supposedly different days of digging. I could go on and on. I have no proof, just my observation. I think they set up on a 10 acre section of woods with all the actors (diggers) and about 50 cameras, and just blundered around for 24 hours, and made a show out of it.