To be clear, if the HIV+ person is under treatment and is "Undetectable", there have been no cases of transmission -- none, never, even with unprotected sex.

Although since medicine never says never, it is still recommended to use condoms.

I have no idea of the transmission rate between an HIV+ person and an as-yet infected person, such research would be unethical in the extreme. But it would depend on the viral load of the infected person, the type of sex, etc. Many factors.

The question of the virus living outside the body is anything from minutes to days (is the area in full sun, is it subjected to temperature differences/extremes, is the area being cleaned at all, etc.). Many factors. One thing would be difficult though is having the virus get from this point into a mucosal lining of another human.

Anyway, I am sure there is context to the question being asked that would allow for a more scientific answer.