Hi Farmer are you under a town code or state code?
OK Normally I use NYC code as it is one of the more stringent codes around so in most area’s it is over kill.
A fixture can be located 2 feet away from the trap and the trap located no more then 2 feet from the vent BUT other codes do allow this distance to vary a lot.
NJ does not have a very good code from what I remember so they may allow this.
IM not sure of your 3″ vent question but on a 3″ vent stack I can run 97 fixture units for a maximum developed length of 250 feet
I size my vent by developed length and fixture units. Some codes do not take developed length into consideration.
I would suggest you look for the local code book in your area. Good luck.
The vent should be above the FLOOD LEVEL rim of the fixture being served at (least 6″ above) and pitched back to the fixture drain to get rid of possible condensation
Hope this helps. Have a great week end