1. What Don saw was a laptop.

2. I don't believe what Don said yesterday.
3. This is what Don wanted to have.

4. What Bill said was not true.
5. I don't have what he asked for.
6. That is not what Bill wanted.

(Are they all grammatical? Check the sentences, please.)

Yes, all six are just fine! Nice.

Yes, all the sentences you provided are grammatically correct. They all follow a similar sentence structure of "What [person] [verb] [complement]." In each sentence, the word "what" is used to introduce a noun clause that functions as the subject or object of the sentence. The verb and complement following "what" provide additional information about that noun clause.