Los Gerundios y Haber + Ado /Ito

Please correct anything that I have misunderstood. Below is my best understanding, but I am not sure that I have it right... Muchas gracias!

He estudiado español
I have studied Spanish (in the past, but not now)

- This sentence may refer that you are studying spanish a little ago too, If you mean in the past it'hs better to say "Yo estudié español" 

Llevo estudiando español
I have been (and am currently) studying Spanish (referring to in general, not that studying was the only thing I was doing)

-This sentence does not sound good to me, it's better to say " Estoy estudiando español" or if you say a period of time "He estudiado español durante X años ..." or "Llevo estudiando español por X años" 

Yo estaba estudiando español
I was studying Spanish (at the time, but not now OR I was studying Spanish very recently in the past)

Yo estaba estudiando español por tres meses
The implication is that the ONLY thing I was doing primarily for the three months was studying Spanish.
- This is wrong, there is no implication of if it's the only thing or not, if you have finished studying (or whatever): "Yo estudié español durante 3 meses" 

Estoy estudiando español
I am studying Spanish (at this very moment)

Yo estudio español desde enero.
I (have been) study(ing) Spanish since June.

-This is correct but to exact translationof your english version is: (Yo) He estado estudiando español desde enero. 

If I am studying Spanish right now, and someone interrupts and asks, “What are you doing?”
I would respond, “Estoy estudiando español” Or maybe “Yo estaba estudiando español, hace que me interrumpiste.”

- The first sounds better, if you say the second "Estaba" has "Yo" implicit, so: "Estaba estudiando español hasta que me interrumpiste" -> Note that this may sound a bit rude. 

If I used to study Spanish in High School, but I have not studied since then, I might say…
“He estudiado español solo cuando yo estaba en escuela”

- Estudie español en el instituto

If I am currently studying Spanish every day to become fluent, and I have been doing this for the past three months, I would say, “Llevo estudiando español port res meses.”

- This sentence it's right but i would say "Hace 3 meses que estudio español" 

Are there any other clarifications that could help me?

-I hope it helps.

I'm studying english now so if I made any mistake correcting you I would apreciate your corrections too.