1. Not a word she didn't say to me.
2. Not that I only mind your behavior, I just hate you.
3. They were here not five minutes ago.
4. The tug crossed our stern not fifty yards away.
5. "Did he have any enemies?" - Not a one. Not a damn one!
6. Not every applicant had a degree.
I think in all the sentences above, "not" is negating the bold parts.
Except in sentence 2, "not" seems to be negating phrases in the other sentences.
Am I right?
fire11. Not a word she didn't say to me.
Not a word did she say to me. (literary)
fire12. Not that I only mind your behavior, I just hate you.
It's not just that I mind your behavior. I hate you.
fire13. They were here not five minutes ago.
Good.
fire14. The tug crossed our stern not fifty yards away.
Good.
fire15. "Did he have any enemies?" - Not a one. Not a damn one!
Good.
fire16. Not every applicant had a degree.
Good.
fire1I think in all the sentences above, "not" is negating the bold parts.
I can only comment on the ones that are natural English, to wit, 3, 4, 5 and 6. I would say you are right except for 6, where it negates "every".
fire1 Can "not" negate phrases and clauses?
Yes. In addition to marking verbal negation, "not" can modify a considerable range of non-verbal elements.