I watched is simple past. To talk about questions or negatives, we need the auxiliary verb "to do". So if you want to ask a question in the past, you say: "Did you watch it?" "Yes, I watched it/Yes, I did." For negatives, it applies to both statements and questions: "Did you not watch it?" "No, I did not watch it/No, I did not." Let's say it's neither of these, what's the real difference if they mean the same thing and you just want to say simply something was watched by me? Ex: 1:"Did you watch the movie?" 2:"Yes, I watched it." 1:"No, you didn't. I know you didn't watch it." 2:"I swear to you, I DID watch it. I really did!" Using "did" instead of just the simple past would put more emphasis on the action, as if you were to say "as a matter of fact/actually/to be honest/the fact is, etc." You can use it this way as well in present tense: 1:"Do you like spicy food?" 2:"Yes, I like spicy food. Why?" 1:"Because I've never seen you eat anything spicy." 2:"I DO like spicy food. I just hardly eat it." I hope this helps!

" I watched" is correct. "I did watch" is not a sentence. "I watched an amazing movie last night"

I did watch is the emphatic past https://open.books4languages.com/english-b1-grammar/chapter/present-and-past-emphatic-tenses/