1. This is correct. Once unlocked, abilities are available indefinitely.
2. Yes, only a single purchase is required to unlock each ability for all suitable girls.
3. Yes, upgrades are personal.
4. Yes, only one ability can be active at a time for each girl (but abilities are party-based you can set a different ability to the same girl under a different party spot).
5. The general consensus is taunt on dodge girls (as well as guts, if/when Nutaku gets the second defensive ability revamp) and attack up on first turn to the rest for most maps.

Extra damage on weakness and taunt on non-dodgers (especially girls like Victoria, who have a "2x skill rate top party if you were attacked last turn" ability after blooming) have seen use in certain specialist maps, like Kodaibana #2 and Re: Ume & Sakura, but Nutaku will get these in 2053 at this rate so you can safely ignore these edge cases.