Do you know any good books that match any these criterias?

the licia troisi the emerged world saga (they're different books and each saga has three books and different protagonist) i really love it :P

Fire, Graceling, or Bitterblue, all by Kirsten Cashore. Good books. Not too much in the superpower department, but Fire (Fire) has mental power and Katsa (Graceling) is raced with survival (fighting, foraging, etc.). Bitterblue doesn't really have a "power".

Any book by Tamora Pierce, though the romance tends to be in the later books of eah quartet.

The Enchanted Forest Chronicles by Patricia Wrede.

Maximum Ride by James Patterson. More sci-fi than fantasy.

Percy Jackson and the Olympians/The Heroes of Olympus by Rick Riordan. The narrater in PJO is a guy, but everything else meets the criteria. His love interest is there almost the entire time.

The Kane Chronicles, also by Rick Riordan. There are two narraters, one of which is a girl.

I am number 4. There isn't a strong female character until the second book though.