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. 

First, please be aware that you're dealing with such subtleties here that you're going to get different answers even from natives. This looks like one of those subjects natives themselves would discuss in a coffee shop.

He estudiado español

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

Estuve estudiando Español or Estudié Español hace un tiempo sound more natural to me.

He estado estudiando Español sounds better, IMHO

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

Sounds good, and an alternative is Estuve estudiando Español. Both would sound a lot more complete if you follow them up with an explanation of why you stopped. Notice that most of the time you can drop the "yo" and sound more natural. 

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 one sounds strange to me. "Estuve estudiando Español por tres meses" sounds better. And if you want to imply that the only thing you did was language study, you might say: "Pasé tres meses estudiando Español", or "Me pasé tres meses estudiando Español". The literal translation would be "I spent three months studying Spanish"

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

Not explicit enough, unless it's answering a "What are you doing right now?" question. You could say: "En este momento estoy estudiando Español" (kinda formal) or "Ahorita estoy estudiando Español" (informal) if you want your WhatsApp friends to stop texting you.

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

Depending on context, it can sound natural, but I would say it a bit more formal: "He estado estudiando Español desde enero." (Oh, and enero is January)

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.”

First one sounds good to me. Second one has a mistake: "hace" should be "hasta". And I'd drop the "Yo".

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”

"Estudié Español en el colegio" would be used in Ecuador. High school has different names in different countries. In Chile it's "liceo" and in Spain it's "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.”

"Llevo tres meses estudiando Español" sounds better.

Are there any other clarifications that could help me?

Read a lot and watch a lot of native stuff. You're very, very advanced for just three months. Keep it up!

Los Gerundios y Haber + Ado /Ito

i`m not sure what you want to say , but  it can be 

-estuve estudiando español  durante 3 meses   

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

Yo estudio español desde enero. ( I would rather say -> (estoy estudiando español desde enero)( he estado estudiando español desde enero) 
I (have been) study(ing) Spanish since June.

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, HASTA  que me interrumpiste.”
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 cuando estaba en la escuela) 

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.” ( llevo 3 meses estudiando español)  

Are there any other clarifications that could help me?