Bad English. We might say "lots of people go", but that wouldn't be an accurate translation.
in the past, when we learned Time, I would see "la Domenica" as "Sundays," like this is a weekly thing. Just "Domenica" seems to refer to a specific (upcoming) Sunday.
I agree. Though in one of my text books, it uses 'il martedi' when it means 'on Tuesday' not 'on Tuesdays' By its own explanation in that particular text it states "The article 'il' is used before days of the week to indicate that something happens regularly on such days." So it is an error on their part to have used 'il' in the text. It beats me how they can get it wrong in a text book!
No, this looks like a habit to me. These people probably go to the stadium often on Sundays. If you were speaking about a particular Sunday, you are maybe(!) right.
Mmm ...really molti vanno allo stadio domenica means domenica prossima (the next Sunday ) molti vanno allo stadio la domenica means molti vanno allo stadio alla domenica ( when is Sunday)