Painted over teak is likely a sign that the previous or current owner was trying to stop leaks.
If this is the case then as Commodave pointed out you should assume leaks and rotted core. You can find the rotted sections as they will feel soft and spongy under foot and if you “sound” the decks with a hammer they sound dull.
Not to scare the bottom paint off of you but I’m in the middle of a complete boat deck replacement right now after a season of “just getting by” with some leaks. In my case it was easier to remove and replace the entire deck (glass over marine plywood) then to fix sections. It’s will depend on how the deck “sandwich” is constructed.
So to answer your questions:
1. It depends. Possible, but you may have leaks and encourage further rot.
2. The fastest way to remove deck involves a small crowbar and a hammer. It’s a destructive process to the teak that leaves the screw heads in place. Then you can remove 1000s of slotted screws with a screwdriver or a pair of needle nose vise grips. Cutting the teak in-between rows of screws with a circular saw helps.
3. Remove them as you’ll need to fill the holes. I only had to cut off 10 in total on my boat deck. The other 2000 unscrewed easily.
4. Yes, then plan to fiberglass over the entire deck. This assumes you’ve repaired any issues with the core.
5. Yes, fiberglass
6. Awlgrip, etc
As others stated already it’s not hard if you have the DIY skills and the stomach for it, it’s just a LOT of labor.
Check out Boatworks Today on YouTube for some videos that will help you get your head around it. Also Sail Life documents a complete re-core of a sailboat on his channel.
Finally get a good survey so you know what you’re getting into with this boat.
A little more on my project if you’re interested (and brave).