1) Jobs available are on the TVA website. That's the only way they hire, there's a nice search function to narrow down to the plants you are interested in. "Advancement" is about like everywhere else; you put in your time, and if you do well enough and are motivated, you will 'advance'.
2) For Ops, it's 12 hour shifts, days and nights alternate weekly, 5 week rotation, training in middle, 8 day break at the end.
3) The pay rates for technical training positions are posted on the TVA website, and they are negotiated by union, so all employees covered by Trades and Labor agreements get the same rate. As far as management goes, degrees and Naval accomplishments are more like minimum consideration qualifications.
4) TVA is a federal government corporation, so what do you think the benefits are like? Seriously, you can find a lot of information on benefits on the TVA website.
5) POSS test is given to as many as 30 candidates all at once in a classroom setting; it's not gonna be an easy transition from Navy to TVA like you want. The jobs that require people to take a POSS are usually only up for about 3-4 days, there's a very small window to apply.
As you can see, at least three of your questions could have been answered if you just went to the TVA website and read the information that was posted there. From that point of view, perhaps you can see why you ended up with some of the responses you got.