Which are the correct verb forms for "eat" when conjugated to the simple past and the past participle? Are my examples correct or not?
Ex:
"I ate."
"I have eaten."

Further, can one use "eat" as a transitive verb with a direct object, or as an intransitive verb without one?
Ex:
"The python has eaten a meal."
"The python has eaten."

Please explain this to me, because I am confused. Thanks.

I think all of your examples are correct. The only thing I would add is that 'eat' is an intransitive verb because it can be used without an object. Just because you can use an object (as you do in one of your examples) does not make it a transitive verb. I hope that makes sense.

Eat is a transitive verb.
I eat cakes.
I ate a horse.

OK. I stand corrected. I guess in the example "The python has eaten" - which is a perfectly correct sentence - the object is implied, i.e. it obviously has to have eaten something even if it is not named.