The principle parts of the verb eat are:
eat infinitive and present
ate past
eaten past participle
eating present participle
Accordingly, perfect constructions are formed with have + eaten:
I have eaten, you had eaten, he will have eaten, &c
Passive constructions are formed with be + eaten:
We are eaten, you were eaten, they will be eaten, &c
Progressive (continuous) constructions are formed with be + eating:
I am eating, you were eating, she will be eating, &c
You will occasionally hear et for the past, and even for the past participle but in US speech these are strictly non-standard dialect forms.
If you go to Oald you'll see that the three basic forms are eat/ate/eaten. "ate" is pronounced /et/ in BrE and /eit/ in AmE. You find the basic forms under the headline "verb forms". – rogermue – 2015-10-03T23:51:36.620
2Haven't ate is certainly something people say, but it's not Standard English. You might hear it, for example, in AAVE. – snailplane – 2013-07-21T04:05:18.567
I have got an Aussie friend and he always says I must have ate something wrong. – user31782 – 2018-11-06T08:06:30.437
Even though it is not related to the question but 'I often use have in place of eat', Have you had lunch yet? I will have it later. – Thor – 2013-03-16T06:33:41.517