re: 8 - no, sort of. The government will get shut down because they have not authorized funding. Sadly, they are likely to make the payroll retroactive to the shutdown date so the folks will likely get paid..
re: 7 - Not my opinion, but it will be the justification. TSA, FEMA, The Coast Guard, Border Patrol, and the Secret Service are all under DHS. There are other functions. If it comes to that, those functions will be declared "essential services".