Non finite clause question

Liz wants to write a novel.

Is this a non-finnite clause? Does this mean that it is not an independent clause and can't stand alone?

How would one punctuate this if attatched to a independent clause then? Is a comma fine?

Can a group of words exist separate from the sentence, by a comma, and not be a phrase or clause? If so, what are they called?

I have learned the types of phrases and clauses that exist; if I want to say additional words that are not part of a clause and are not joined by a conjunction, and don't seem to be one of the phrases I hve leaned, what can they be?

Hope this is understandable.

Here is an example of what I mean possibly: I ran down the field, with or without the defender. The italicized words; what are they?

Thanks.