Hi, I'm a professional Resume writer located in the USA, and I am
looking to gather more information regarding resumes for teachers.

What do school administrators/teacher search committees look for in a
candidate? What's important?  What's not?

Is a "Philosophy of Education Statement" necessary to submit to
potential employers?

Are there unique tricks that are specifically used on teacher resumes
vs. resumes for other jobs? (Basically, are they any different than
resumes for other professions?)

What exactly is a Cirriculum Vitae (CV) and when is it used?

I do not need 'basic' info on how to write a resume, or samples of
resumes (unless it's necessary to answer the question with an
example).

Thanks!

Perhaps this definition of curriculum vitae is of help:

"A special type of resume traditionally used within the academic
community. Earned degrees, teaching and research experience,
publications, presentations, and related activities are featured.
Unlike a resume, a CV tends to be longer and more informational than
promotional in tone. Note: The CV required in theses and dissertations
follows a very specific format."
gradschool.uoregon.edu/glossary.html

You're a professional Resume writer and you don't know what a Cirriculum Vitae is?

Good blimey! :D

I don't know about the US but here in Australia an application for a
teaching position usually requires that application to address
specific selection criteria.

Curriculum Vitae (note the correct spelling of curriculum, not
"cirriculum") is Latin for "course of life" and generally contains  a
summary of your bio, education, and work history.

A Philosophy of Education statement would be entirely appropriate to
include. Having assessed applications from teachers in the past, let
me tell you that spelling mistakes are a big no-no!

Note also that the plural of Curriculum Vitae is Curricula Vitae.

I second amoobangkok-ga's comment.  How can you make your living
writing resumes without knowing what a CV is?  Granted, they are
rarely used in the U.S., but that's no excuse.