That feature is only active from about level 1-6. It will stop after a little while, just ignore it.
Do Quests.
Kill stuff, do quests and chat
As of Patch 3.1 of World of Warcraft, there are no longer any "daily" quests in Wintergrasp. They've been moved to being "weekly" quests. There's a lot of information about the quests in Wintergrasp, including the random weekly quest players will want to hunt down. See the link to WoWWiki's page on Wintergrasp Quests to get the full deal.
You get experience by either killing monsters or doing quests.
You must do a lot of quests and go to Raids and Dungeons!
Yes, World of Warcraft is violent - but the violence is not explicit and it not the only thing in the game - there are quests and professions that are not violent.
Simple, talk to the NPC's (non-player characters) with the yellow ! over their head. They are the ones that give you quests. There are also things that drop off mobs that will sometimes give you quests.
Generally, the quests you do in Brill will lead you to quests in other zones that are good for you as you continue to level up. In this case, Brill quests will lead you to The Sepulcher in Silverpine Forest, which is south of Tirisfal Glades.
Humanoids drop gold when killed, and it can also be obtained from chests and quests.
There are three ways. You can kill things, you can do quests, and you can do both at the same time
You need to be level 70, and have your epic flying training.
Probably do daily quests or heroic instances :)