You're just flat out wrong. Government employees are backed by one of the strongest unions in the country and the union fights every damned attempt to fire someone - whether they are in the wrong or not. Check the numbers.
No, I'm not. There is not a single union that oversees all government employees, especially those in critical positions. Again, look at the Air Traffic Controllers. These guys are paid well, professionally trained, and can be removed from the job easily when they show incompetence.