Is watching movies in the cinema forbidden due to its Jewish founding, the intermingling [of sexes], and the nature of the films shown? And is it permissible to enter a cinema to watch matches?

This statement is generally correct, because the ruling on movie theaters depends on what is shown in them and the condition of their patrons. If we assume they are free of forbidden things such as intermingling and obscene language when watching matches, then the consideration remains whether the conditions for permissibility of watching these matches themselves are met, bearing in mind that encouraging sports teams and following their matches in the usual manner involves evils that a Muslim must abandon.