Each Wizard gets Training Points that they can spend on spells in other schools.
You will receive one training point every 4 levels till 20. After level 20, you will receive one training point every 5 levels. You can also receive training points through certain quests.
These training points can be used to learn spells from outside your school of focus. In order to learn higher level spells of a school, you have to first learn the lower level spells.
She's right. But there is an exception. For certain trainers like Sabrina Greenstar in the fairgrounds, and Mildred Farseer in Colossus Blvd., all you have to do to learn the spell is be a certain level (i.e. you have to be at least Lv.10 to learn the shields from Sabrina).
If your not happy with your choices, then at I believe Lv.10, you can spend crowns at the registrar in Golem Court to buy back all of your training points (crown costs depends on how many training points you've spent).