Yes it is. Click the following link (below) and scroll down the list until you see the word "post-".
http://www.umt.edu/urelations/style/p.htm
In this case, post is a prefix, not a standalone word. Therefore, it should be properly hyphenated as post-secondary.
Ordinarily it is spelled as the hyphenated form "post-secondary."
No it's not hyphenated.
College is considered post-secondary education.
Post secondary education is the educational level following the completion of a school providing a secondary education. This would include high school (secondary school). Thus, any degree in higher education following secondary school is considered post secondary, if not then it is not post secondary.
No, "post procedure" is typically not hyphenated in standard usage. It is used as two separate words to describe something that occurs after a procedure. However, in some specific contexts or style guides, it may be hyphenated as "post-procedure" when used as a compound adjective before a noun (e.g., post-procedure care). Always check the relevant style guide for specific usage.
I have attended two post-secondary schools.
post-war pick-me-up
when you learn about post
The short answer is yes. It varies from organization to organization, but most of the medical sites I visited hyphenate post-traumatic.
Yes, college is considered a form of post-secondary education.
Yes it is. If a school is a college or university, it is a post secondary institution.