Is a student's collective noun or common noun?

"A student" is a common noun. In your example, you have an apostrophe, so it is actually being used as possessive.

The student's book was on the chair.

Apostrophes are never used for plurals unless you are talking about single letters, like grades, and it would be a different word if you just added an -s to the end.

Example: On her report card, Mary got mostly A's and a few Bs.

You use the apostrophe for A's because it could be confused for the word "As". There is no word "Bs", so you don't use an apostrophe to make it plural.

Collective nouns are those which mean a whole group of people or things in one word. Some examples:

Congress (many people in one Congress)
jury (usually 12 people)
committee (more than one person)

Hope this helps!