Is just "no." a valid sentence? [duplicate]

Yes.

Single-word sentences are fine, because subjects and predicates can be implied.

If we were driving in a car, and you kept singing an annoying ad jingle over and over again, I might say, "Stop!"

"Stop!" is a one-word sentence. The subject (you) is implied. It's essentially a shortened version of, "Will you please stop singing that song!"

Contextually, it would be obvious that I was asking you to stop, not the car. It would be obvious that I was asking you to stop singing, not stop breathing. Hence, I don't need to add those words, just to make it a sentence. I simply yell, "Stop!" and you figure out the rest.