"Are there class trainers in the Outlands?"
No, there are no class trainers in the Outlands. Each class now has trainable talents at odd levels, so it may be necessary to port back to a major city in the Eastern Kingdom or Kalimdor every level. No Auction House, either. There's a bank in Shattrath. Yes, just Shattrath. Remember all that "get the Flight Point" info earlier? Shattrath is your easiest, fastest, no-hassle way to all of those conveniences.
"Will you socket this gem for me?"
Ok. Jewelcrafting. It's one of the new professions, and once you hit 70 it's really useful. But let's clear up a few misconceptions. It's not enchanting. Jewelcrafters can't socket an item in the "do not trade" slot. They can't socket anything for you. They can cut gems and trade you for them so you can socket it yourself. To get to the socket screen, hold shift and right click on the item. You can remove gems from a piece of gear but the process will destroy the gems. Socketed gear below level 65 is not worth spending a great deal of money on, as you will replace it right away.