Is what my friend did, imitating sodomites—Allah forbid—as a joke, considered an act of sodomy, and must I distance myself from him? And will I be held accountable for my father unintentionally seeing my private parts when I was ten years old?

Your friend's action is forbidden, even if it was a joke, and you are rewarded for advising him and enjoining him from evil.

Homosexuality has different types and degrees. If your friend abandons this act and his situation improves, you are not obligated to distance yourself from him. However, if he does not abandon it, or if you fear him, then distance yourself from him.

Looking at the severe nakedness (private parts) of someone who has reached the age of ten is forbidden. As for merely seeing it unintentionally, there is no sin in it, for Allah Almighty says: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts have intended." And a boy who has not reached puberty is not held accountable, for the Prophet, peace and blessings be upon him, said: "The pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches puberty, and from the insane person until he regains his sanity." Therefore, there is no sin upon you.