What should I do about knowing that my father—the muezzin of the mosque for 20 years—flirts with widowed and divorced women and is addicted to mobile applications that display immoral pictures and videos?

You should be certain before accusing your father of reprehensible acts, and beware of assumptions, as the default for a Muslim is blamelessness and good assumptions. If his commission of reprehensible acts is confirmed, then he must be enjoined to good and forbidden from evil gently and discreetly, along with supplicating for him. Enjoining one's father differs from enjoining others; he must be taught without violence, abuse, or harshness in speech, otherwise, he should be left alone.