On pve servers the NPCs are camped instead, so you can't accept quests or turn any in. So, the situation is similar to what OP experiences on pvp realm, inability to level properly.
It's not about "well, it's pvp server!" response to OP, the issue is griefers.
The solution should be penalties. If u kill a gray level player, you get dishonor and a debuff that stacks to 10. Once you reach 10, you get crazy amount of dishonor so in short time you will loose all your honor, hell you will get minus honor so next time you want to buy something with honor, you won't even start from zero
The same should be done on gray level NPC's to prevent griefing as well, instead for dishonor, they loose Justice Points, yes I said it, JP you will loose, and once debuff stacks to 10,
YOU WILL LOOSE VALOR POINTS!
Oh, the horror!!! PvP players forced to fight similar lvl players for fairness! Omg let the qq begin by loosers that can't kill anyone their own level.