I can still do some exploring in the Straits, but from the looks of it I either have to do the events or some old fashioned grinding. Or am I missing something here?
Mob farming is far and away the least efficient way to level up. You get far more EXP from doing meta event chains, or from doing PvP and getting tomes of knowledge that raise your level by 1 per tome used.
And how exactly do armor stats work?
There are only five (maybe six) types of gear that really matter in GW2.
For general PvE play, you're almost always going to be using either berserker gear (stats tailored for maximizing power based damage), or viper gear (stats tailored for maximizing condition based damage). This might be too glass cannony for HoT expansion maps, as the mobs there are much more dangerous. If you die a lot in HoT maps and adding more defensive abilities and traits to your build isn't helping, then consider getting gear with Marauder or Trailblazer's stats. They deal a little less damage than Berserker/Viper but give you a 25-30% HP increase that can allow you to survive a few more hits.
Celestial gear has the highest stat total, but that number is spread out evenly among all stats and there are only a few builds that can effectively benefit from such a spread of stats.
For WvW gameplay, you usually want to wear marauder, trailblazer, or celestial gear, since they give you more survivability. Glass canon stats like Berserker and Vipers are generally not recommended there because of the low time-to-kill. You could die in less than two seconds wearing those glass canon armors.
If you play a healer build (for WvW zergs, or for the small handful of PvE raids in the game), then you can wear Minstrel's gear.
Sometimes theorycrafters will swap out one or two pieces of gear with an alternative, ie replacing a couple pieces of your marauder set with dragon gear (same stat total but just shuffles the numbers around) for minmaxxing purposes. Ie you've hit crit cap and thus you wear a couple of different pieces of gear that give you stats in other areas rather than just letting those excess crit points going to waste. But minmaxxing to this degree is irrelevant to the vast majority of players. Minmaxxing DPS only matters if you are PUGing the highest end Fractals or something. The highest DPS check you will encounter in average play is the paltry 5k DPS check for the Dragon's End meta event final boss at the climax of the End of Dragons expansion, which anyone can hit if they aren't AFK, and even if there are AFK the showoffs pushing 40k DPS will singlehandedly carry all of the AFKers anyway. If you fail Dragon's End, it's not because of a lack of DPS. You either got screwed by bad RNG and the boss went into too many invincibility phases, or people botched a mechanic. Lack of DPS is almost never an issue in GW2 like it is in WoW or in FF14.
As for runes, use the Fireworks set until you reach the PoF expansion and acquire mounts. It gives you a passive +25% movement speed so you don't have to waste one of your ability slots on a movement speed signet. Runes are being reworked when the new mini expansion arrives at the end of the month so don't sink a lot of money on them.