Let's start with the first one. At home, they undress so that nothing hinders movement and to feel comfortable after a day in tight, formal clothes. Many friends walk around the house in shorts and socks, personally I never understood this because I have loose clothes especially for the house. But this is everyone's choice. On the street, people go naked for several reasons: firstly, it happens in the summer and the men undress to sweat less, personally I have profuse sweating and no means of protection help; secondly, it seems to me that this comes from lack of culture. I do not think that in big cities you often meet an unclothed man, this is mainly a disease in provincial cities, where people treat each other more easily and are not ashamed to behave "at home". Personally, in my youth, I allowed myself this, now I have apparently become more responsible and I know where you can walk without a top, and where you need to be stricter.
They walk half naked, because their house of the day symbolizes a relaxed home environment in which you can walk as you want and feel relaxed. Anyway, after work it's nice to throw off your clothes and flaunt in your underpants.
I also go half naked at home. Also, I am NOT fat or gay.