Forget the food and water you get from kills.
As a mage you can make your own, so first thing you do on logging in next time and every time is to create a stack or three of water, this replenishes your mana, just like the spring water you buy. Conjure food (sweetrolls, I think) and use that to eat between fights. Conjured food and drink items vanish if you stay logged out for more than 15 minutes. For the cost of some mana, you don't have to spend money on food. Tip: you can both eat and drink at the same time.
As far as skills go, you learn new ones or higher versions of older ones at every even level. Your class trainers are everywhere almost, on Northshire Abbey, Library; In Goldshire, Inn second floor; and in SW City, Mage Quarter at the top of the tower.
Just ask a guard for directions.
As far as professions go, absolutely learn all three secondary ones, those are First Aid, Cooking, and Fishing.
As a mage you might want Tailoring/Enchanting ..but you won't be able to make full use of them in a trial version, nor can you use the auction house while running trial.
At your level you should have the Arcane Intellect buff available as well as (I forget the exact name) Frost armor or something like that. Cast both on yourself at all times, and cast the intellect buff on any Pally, mage, priest, shammy, lock you see. Most people with buff abilities freely cast on others. It's a good way to make friends.