Is the money spent by the father considered permissible or impermissible, given that a portion of his income comes from renting out spaces to individuals who engage in illicit activities, and is it permissible for the son to benefit from this money?

So long as your father's money is mixed and not entirely unlawful, what he spends on his children is lawful for them, and it is permissible for you to benefit from it. Your earnings from tailoring are also lawful. Your father must prohibit tenants from selling unlawful things, and if they do not desist, he must terminate the contract whenever he is able, and he must dispose of the unlawful rent.