While i understand the learning aspect of this phrase - i think it's important to note that most conversations people would simply say: 'Понятно?' - which means the same as 'Ты меня понимаешь' (Understood?/Is it understood?)
Actually, 'Понятно?' does not mean quite the same as 'Ты меня понимаешь?'. Specifically, there is no "меня" (me) part, explicit or even implied. 'Понятно?'="Is is clear?", it can equally well refer to something I've just said or to a passage in a textbook. In the latter case 'Ты меня понимаешь?' would be simply inapplicable.
Yep. In fact all of the personal pronouns (меня, тебя, его, её, нас, вас, их) are the same in both genitive and accusative.
У него нет кошки. У неё есть кошка. У них нет ни кошки, ни собaки. (In genitive case).
It is not that "него" is the "pure" genitive so to call it, which is still "его", just that after (many? all?) prepositions (like "у"), the "н" is added to those pronouns in the genitive (for ease of pronunciation I guess...).
For example, Duolingo has taught us that "нет" requires genitive, so "he is not by me" / "I do not have him" would be (as far as I can tell):
"У меня нет его" or "У меня его нет" (not sure about word order)
Not "него", because there is no preposition acting on "его".
So this is accusative? It merely looks like genitive because меня is the same in both cases?
Yes, both statements are correct. "Меня" is accusative here (the most natural case for a direct object) but its genitive form is identical.
Lol I guess this is how Red Boyou yells at the Waterboy in Russian:
"DO YOU UNDERSTAND ME!??"
I heard the phrase 'Ты меня понял?' - can I use it equally to 'Ты меня понимаешь'? Is понял simply a short version or what is it?
It's not a short version, it's the past tense of perfective verb "понять". As a perfective verb, it does not have a present tense. As a result English "Do you understand me?" can be translated as either "Ты меня понимаешь?", which more literally corresponds to "Are you understanding me" or "Ты меня понял?", which literally corresponds to "Have you understood/did you understand me?".