Eunuchs may be gay or straight.
No. A gay man is someone who is sexually attracted to other men. A eunuch is a castrated man (who may be gay or straight).
Gay men are already men.
Gay men are individuals who are attracted to other men romantically and/or sexually. Sexual orientation (being gay) does not influence someone's gender identity (being a man). Men, whether straight or gay, identify as male based on their self-perception and expression.
Here is the only real fact: men cannot become gay. They are born that way.
Nobody can "become: gay. Sexual orientation is not changeable. It works the same for both men and women.
No, eunuchs are typically individuals who have been castrated and therefore cannot become pregnant as they do not have functioning reproductive organs.
Yes, but only gay women. Gay men cannot.
No. He made himself a eunuch for the kingdom of heaven's sake: Matthew 19.12. For there are some eunuchs, which were so born from [their] mother's womb: and there are some eunuchs, which were made eunuchs of men: and there be eunuchs, which have made themselves eunuchs for the kingdom of heaven's sake. He that is able to receive [it], let him receive [it].
No. gay men cannot become straight, just as straight men cannot become gay. Gay men can choose to be celibate. They can even convince themselves that they aren't gay and get married, but they are still gay.
No straight person becomes gay. Ever. You are either born gay or you aren't.
One does not "become" gay. Your are born with your sexuality. You can experiment with the same sex, however, this will not make you gay.