Yes as ALL fixtures need to have the vent placed above the FLOOD LEVEL RIM
Every toilet needs to be vented.
The highest 4 inch pipe should have a vent on it, or directly above a toilet junction Above the flood level rim of the fixture it is servicing IT does not mean the toilet
Yes. If not it will be a wet vent and cause MAJOR problems.
Yes if the vent pipe is 4" and vertical by code and there is nothing connected between your toilet tee and where you would connect your new toilet tee. If not worried about codes then yes you can connect to a 3" vent line if no other vent lines are connected down stream. If you have a vent pipe that is less then 3" and or you have other vents connected between your old toilet tee and your new toilet tee then NO you can not connect a new tee for your toilet.
No
Who needs a toilet
Within 24 "
Yes.
partially clogged drain or vent, improperly installed vent or drain
Within 24 "
Any vent is usually the size of the drain or waste pipe it is connected to. 3 or 4 inch on a toilet.
Should be individually vented
As close as possible is best, but there just has to be a vent so that the air that is in the line has somewhere to go so that the liquid isn't trying to compress it. The closer the vent is to the toilet, the better it will flush.