Hi! The verb учиться is followed by the questions что делать?(what to do) где?(where) Example: Я учусь играТЬ на гитаре. Я учусь танцеваТЬ. Example for где: Я учусь в университетЕ. Я учусь в России. As you see this verb is followed by the prepositions and noun in prepositional case when you speak about place (В России, В Китае, В университете). The verb изучать is followed by the question что?(what) and noun in accusative without prepositions. The meaning of it is to learn the object in details, carefully. Example: Я изучаю историю Китая. Я изучаю русский язык. Я изучаю экономику. So, about your examples, as you see, "Я изучаю по-русски" and "Я учусь по-русски" have no difference because both of them are incorrect. По-русски is an adverb, you may say Я говорю по-русски (I can speak russian). Good luck!

After the verb учиться you should use a verb in infinitive (я учусь говорить по-русски) or a noun in ablative (кому? чему?) (я учусь русскому языку). After the verb изучать you can use only a noun in accusative (кого? что?) ( я изучаю русский язык).

изучать is used when you are speaking of one subject of study (math, a language,). Учусь is used when you are talking about the process of being educated, (either as a profession, place of study.) Я учусь в Московском Университете. Я изучаю русский язык. Hope that helps.

Изучать - means deep... Я изучаю поведение животных (I have been studying the behavior of animals) . You can't say - я учу поведение животных. But you can say - я учусь в школе (I am learning in school )

You can study\research someone's behavior under certain conditions. That would be: изучаю поведение в определенных условиях Here you would neither use learn nor учу. That's the main difference which is parallel in English and in Russian. In other cases you can use either учу\изучаю. Я учу\изучаю русский.