If both balls of a man be removed, can he still masturbate? whether he loses his mustache and turns out to a woman, morally? can he even be alive?

Depends: Unless he receives externally injected testosterone to maintain his interest in "sex" there would be no drive to masturbate. He would not produce sperm, but could expel some prostate secretions if he achieved erection & orgasm. There are a lot of things a male could succeed at with bilateral nut loss, but it would take some outside help.

Testicle loss: in addition to the excellent information other doctors have provided, please consider that you are still a man, a human being, and someone who can lead a good life w/out testicles. Of course what you have have been through is traumatic but many others loose body parts and look deeper into themselves to find meaning. Peace and good health.