What suffix would be added to the end of a verb to make as it is being done (I'm eating), or that it has been done (I have eaten, I've ate). For example 私は食べる, or I eat, 食べる would be converted into what to make it, I have eaten and I'm eating?
In general, trying to translate specific sentences from English into Japanese isn't the best way to learn Japanese grammar (although it can be part of a greater experience). Japanese grammar doesn't work exactly the same as English grammar and has different "building blocks", so things don't always translate directly over. Nevertheless, here are how you would do the progressive and perfect in Japanese.
The progressive aspect in English has a pretty direct equivalent in Japanese. Namely, it is the 〜て form of the verb followed by the auxiliary verb いる (note, the い is commonly dropped). In the case of たべる it would be たべている.
Here is a full derivation for たべる (tabe-ru):
Here is a derivation of something with an uglier 〜て form for fun, かく (kak-u):
The perfect aspect in English is one of those things that does not have a direct equivalent in Japanese grammar. So, to figure out how to translate the perfect, we need to break down what the perfect is used for in English by meaning: