Yes, you can. It would be more natural to say 'I have dinner at exactly six o'clock', though. We put the word 'exactly' before the number.

Yes, you can. Your sentence makes perfect sense. :)

You may use exactly, However if you are inviting friends for a 6:00 pm dinner and you say exactly, you are saying "Don't be late". I expect you to be here no later than 6. It is grammatically correct, but a little strongly worded. If you are talking about when you eat, I eat at 6 every night is fine as well.

There's also "I eat a 6 o'clock sharp." A phrase that means the same thing.

надо "at 6 o'clock sharp"