It can indeed be used for tuition, books, and housing, yes.
Can you explain to me the requirements in applying for tuition assistance if I am approved for federal TA?
You meet the two requirements listed below.  Both must be true:  You qualify for the Montgomery GI Bill Active Duty MGIB - AD or Post-9/11 GI Bill benefits, and   The cost of the course and fees is more than what TA will cover.
What specifications are we discussing?