Olaf's very unusual science project. a fragment or complete sentence?

Fragment.

Explanation:

There is a subject, Olaf's very unusual science project, but no predicate, which is the action. We know what is doing something, but we don't know what it is doing.

An independent clause is a group of words that contains a subject and verb and expresses a complete thought. An independent clause is a sentence.

here are a few examples of what an independent clause is;

The beach is a lot of fun, yet the mountains are better.

A group of us went to the movie, and we agreed it was enjoyable.

I went to the store, but I forgot to bring my shopping list.