Busking in Azerbaijan is really hard, since the people don't really understand the point of it. Another problem would be the the police, because busking is considered begging if you do it for money, so it would cause a lot of trouble. The currency in Azerbaijan consists of Manat(1 Manat is around 1 Dollar) and Gapig, but people will mostly drop a paper of 1 Manat. Playing in the center of Baku is the best choice, but it is always patrolled by police and if they see you playing for money, they will instantly approach you and probably take you to the station. Nothing much will happen, but you will spend around two hours answering questions. It's even harder to busk in other cities, since the people are not used to the idea of it, so they'll probably just walk away with out even noticing or paying attention to you.
Most nationalities need a visa for Azerbaijan. A tourist visa usually costs 60 € anywhere in the world (130$ for Americans). You can enter the country within 30 days after issuing and stay for 30 days from the day of entering the country.
If you have a stamp of Nagorno-Karabakh in you passport, entry will be denied, even with a valid visa.
If you have an Armenian visa in your passport, you will have to answer a lot of questions at the border, which might take up to an hour. You can still enter though.
Where to get it
If you want to apply in Tbilisi, you will need a letter of invitation, which will cost you about 120$ additionally. It's better to apply at the consulate in Batumi, where you can get it without any hassle within 3 working days.