I'm asking about the grammatical form makan vs. memakan. Does it have a different function from tulis vs. menulis? When is the prefix "me" used? Here it looks like "menulis" is used as a transitive verb with an object. If there is no object in the sentence, would it be something like: "saya tulis" vs "saya menulis surat"?
The formal form (when giving a speech, writing, etc) is to add the me- prefix to make the verb. In spoken language it can be left out without necessarily changing the meaning. It's the same transformation with memakan/menulis but depending on the root it doesn't always give the same result.
For intransitive verbs there is another prefix ber-