Is it permissible to pray Jumu'ah (Friday prayer) at home, alone or with brothers, and is one who does not go to the mosque to perform it sinful, considering the excuse of bowed legs and the difficulty of going out and mingling with people?

We have previously clarified the ruling on Friday prayer for a disabled person, and the summary is that he is obligated to attend it if he can do so without hardship or harm; otherwise, it is not obligatory for him. Your situation is easier than that of a disabled person. If you are able to reach it by yourself or with the help of others, it becomes obligatory for you; otherwise, it is not. Your lack of accustomedness to mingling with strangers or fear of embarrassment is not an excuse, especially since the sermon time is short.