alot
Yes, there are many.
Thousands, at least.
Many rabbis were killed.
It's mostly Orthodox rabbis who are multi-generational rabbis.
No. Very many do (some trimmed, some not trimmed), but there's no requirement, and customs in the various communities differ.
I believe rabbis CAN be scribes.
Rabbis are men. They do not get pregnant.
Keshet Rabbis was created in 2003.
No, there are female rabbis, even amongst the Orthodox. (Orthodox female rabbis aren't pulpit rabbis.)
Rabbis are allowed to do and not do the exact same things as any other Jewish male. There are not any additional restrictions placed on rabbis.
Rabbis are teachers and clergy people.