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.
No, never!
There are no issues with being in pictures in Judaism.
Weddings and divorcesAnnulling vowsDeciding the Jewish law in obscure or new cases
yes Yes, as of the 1970's, there have been women ordained as rabbis.
Yes. Reform Judaism has allowed for female Rabbis for over 50 years.
It's mostly Orthodox rabbis who are multi-generational rabbis.
Yes. They were Jewish rabbis, and they were/are allowed to marry. Since Jesus Christ did not marry, many Christian priests do not marry, but, there are a lot of Christian priest that do get married.
Rabbis are men. They do not get pregnant.
I believe rabbis CAN be scribes.
Keshet Rabbis was created in 2003.
No, there are female rabbis, even amongst the Orthodox. (Orthodox female rabbis aren't pulpit rabbis.)
Rabbis are teachers and clergy people.