One thing about writing in fingerings: on occasion you may find that you prefer to use different fingerings from your stand partner. (This is especially true for violists as hand size matters more!) When writing in fingerings, write them above the staff if you are seated outside, and below the staff if you are seated inside.
Normally, stand partners decide whose music to use at the first rehearsal.
Typically we work out fingerings at home and copy them into the part being used before rehearsal. Sometimes things get written in during rehearsal (bowings, fingerings, etc.) and need to be copied into the part that goes home. With experience, it shouldn't take more than a few minutes before or after rehearsal.
Unless the material to be written in is actively discussed in rehearsal, orchestras don't normally stop to allow people to write things in. If necessary, one may have to stop playing in order to write something in, then jump back into playing.