The hearts are there simply to warm you up to playing the game. As you guys get into higher level maps, you will see fewer and fewer hearts til you get to the Orr maps, which have no hearts. Here are some other ways you guys can level up: Map completion: This means getting all the hearts, vistas, PoI, Hero Challenges, and waypoints in the map.
Masteries are account wide, so you can work on them on any character that's level 80. If you get a mount on one character you have it on all your characters, even lower level ones. Same with gliding. Hero points are how you unlock your elite spec, which to some degree changes the way you play your character. Op, as others mentioned, without any hero points (HP), at level 80 you will unlock all 5 core lines and all utilities. Additional hero points can be found and earned through Tyria, HoT and PoF maps (but not Living World maps). Tyria HP are everywhere, but only provide 1 point. PoF and HoT HP are much less, but provide 10 HP each. Level Boosts. Level 80 Boosts come with the expansions and can also be bought in the gemstore. These boost your character directly to level 80 in addition to granting them a basic set of starting gear. The gear and build granted to you by a level 80 boost is typically very poor but will suffice while you get your start as a fresh level 80.
