I've personally used TNet for all my multiplayer projects and it's been the best multiplayer package to work with. I can answer some of your questions ...
- Would TNet work fine for a fast paced shooter based game?
I don't see why not - I've used it for a top down shoot em up multiplayer game and it's been perfect.
- My game has Online / Local Multiplayer, can TNet handle this without me having to write separate code for Online / Local Multiplayer?
Yep, like devomage said, as long as you code it right it should be seamless.
- Does TNet have a Master Server? Or is it able to work with the Master Server Framework found on the asset store?
Yes the master server is built in.
- Is TNet able to work on other platforms besides Windows such as Xbox One, PS4, Nintendo Switch?
Yes, though not out of the box. I can't get into specifics, but TNet supplies the source code. So with some minor adjustments porting to consoles isn't a huge undertaking.
Hope that helps!