Could Not Eat or Ate?

The tense of the verb does not matter - it is the way that the negative is formed that matters: 1. Not is an adverb and should follow the verb: "I ate not the food because I wasn't hungry." About 400 years ago, and earlier, this is how English was spoken, and that sentence would have been correct.

Could eat or could ate?

Only #2 is correct. The Present Perfect tense uses the auxiliary verb 'have' + the past participle of the main verb. The past participle of the main verb 'eat' is eaten', not 'ate'.

Which is correct I have eaten or I have ate?

In standard English, the past participle form of eat is always eaten. Ate is the simple past form. In the perfect tenses, which are indicated by has, had and have, you will always use eaten, even in questions where has, had or have has moved to the front of the sentence away from the verb: I eat, we eat, Jeff eats.