I have been studying English for 10 years. - CORRECT I have been working with Business Administration since 2005. - CORRECT I had lived in Australia, but since last year, I have been living in Brazil. Should read as 'I lived in Australia, but since last year, I have been living in Brazil'. Past Simple is suitable here because the action is completed. We use past perfect when you are talking about a time in the past but then want to refer to a time before that. For example: I hated speaking English until very recently (PAST SIMPLE - completed action), I had lived in Australia for 2 years (GOING FURTHER INTO THE PAST) and found it very difficult to understand what people were saying

Thanks, Andrew! It was very helpful! =)

You can also use the construction "I used to live in Australia but, since last year, I have been living in Brazil." In the case of both your first sentence and the second part of your second sentence, the tense assumes that these things are true about you right now - that you are still studying English and that you are living in Brazil now. With the final sentence, it is more common in English to use the preposition "in," rather than with when we are talking about an area of work, as opposed to the type of people with whom you work. So, we say: "I have been working *in* Business Administration," but we would say "I have been working *with* doctors, for example.