dude! what a killer post!
The favelas were built on preservation areas, like the national parks in the US. But like everything in Brazil is out of control, it all starts with one person breaking in and building and then others will follow and the authorities didn't do anything about it at the time. Now the problem is so big that it became impossible to turn back and remove all those people from those illegal constructions. They don't pay taxes because they are all illegal. All those houses are built with no regulations and some are risky to live in. They are also not free, most are "owned" by people who just took advantage of the situation and built many of them to rent out. It's just completely out of control, these areas are usually dominated by drug lords or militias, and they have their own laws. If you want to see (visit) a curiosity, there is a park called Catacumba, in Lagoa district. There was a favela there in the 60's or 70's that was removed by public authorities, now it's just forest with hiking trails, but you can still find some favela houses lost in the middle of the forest in the trails.
The bananas is also a common thing that all foreigners say when they go to Brazil, it's a different type of bananas, called "banana prata" that I've only seen in Brazil. I don't know why they are not exported, but my guess would be that they probably don't last long for long trips to be exported as the ones you usually see in the US. But we also have the type you see in the US, when you go to the market look for "banana d'água", it's the same one you find in the US.
What a great start! Hope you enjoy the rest of your trip as much as your first day.