I'm completely internet taught, so there are large gaps in my theory knowledge, and I don't have a teacher to ask about my specific misunderstandings, so I'm sorry if this is a novice question.
If I were to play an E and an Ab that would be an E major. However, if I were to play the same Ab and the E above that, is it still an E major? Or is it a different chord entirely, with the Ab as the root?
Uhm, no... E and Ab would not be an E major. For one thing, a chord by definition is 3 notes or more. Therefore "power chord" is a misnomer since it is technically only two notes (usually, the root and the perfect fifth. The octave doesn't count as a third note since it is the same note as the root).
E and Ab would form a major third interval, but not a major chord.
The three notes that make up a major are: the root, the major third, and the fifth. For E, that would be: E, G# (ie Ab), and B.
If your question is about the interval from an Ab to an E as opposed to an E to an Ab, the answer is:
E to Ab = major third
Ab to E = sharpened fifth
Depending on which is lower and which is higher, their interval relationships change. However, if you are composing a major chord (in this case: E, Ab, B), you can make a chord as long as those notes are involved.
The typical E major chord:
6 strings, but only 3 notes. Specifically 3 Es, 2 Bs, and 1 G#/Ab. The three Es are on the low E, high E, and D. The two Bs on the A and B. The one Ab on the G.
To make it minor, all you have to do is flatten the single Ab/G# to a G.