"Yes, I study here."
Translation:Да, я учусь здесь.
Though it's true and sometimes personal pronouns can be omitted in Russian, it is too hard for not native speakers to decide can it be omitted or not in a certain case. So if you don't sure, it would be better to always use personal pronouns in sentences. It will be correct and understandable.
Here's a sample with учучсь without personal pronouns:
-Привет, не ожидал тебя встретить, ты что здесь делаешь?
-На кого учишься?
Russian isn't a pro-drop language to the same extent Spanish and Latin are. There are certain cases in Russian where you can drop the pronoun, but as a general rule you can't.
Though I would like a mod to chime in and tell us when dropping a pronoun is okay in formal, written Russian. Because though English is a strictly non-pro-drop language, that doesn't stop English speakers from dropping pronouns in colloquial discourse. E.g.:
"Want to go to the park?"
"Can't. Got stuff to do today."
With or without "Да,"?
I would still say that they are interchangeable. Placing both "здесь" and "тут" at the end or in the middle of a sentence slightly affects its meaning in exactly the same way. "Я здесь/тут учусь" looks more like a neutral statement. In "Я учусь здесь/тут" "здесь/тут" becomes stressed.
It seems that the main Russian translation above has been altered since the moment that you asked your question.
Я учусь в этой школе/в этом университете. (Is almost the same as "I attend this school/university" but not literally. The literal translation is I learn/study there).
Я учусь русскому языку. (I am learning Russian) Also Я учу русский язык.
Я учу русскому языку. (I teach Russian)
Edit: The more I attempt to answer, the more complicated it seems to get even for me :-)
Я учу русский язык = I am learning Russian (it's probably the most frequent way of saying it).
Я учу русскому языку = I teach Russian
Whenever you use учусь it is you who is learning (the only question can be where or what).
If I fail to cover it in one comment feel free to ask more questions. Also on my stream.