Need advice on main stack location and toilet to stack distance.

The toilet is being moved 13 feet (total pipe distance) 6 feet 4" and 7 feet 3".
The house has a 4 inch main drain and the toilet will be reconnected using a 3" pipe to reconnect into the main drain.
The new toilet location would be moving upstream 6 feet from the original vent location and the 7 feet of 3 inch pipe would be a new lateral connection.

I understand there is a minimum distance between the Main Vent and toilet.

1st question:
If the main vent is not within this minimum distance can the toilet be vented to the main vent using 2" vent pipe instead of the 3 inch pipe the toilet will be connected to?

2nd question:
If the main vent distance is questionable for proper venting, could a 2 inch vent to toilet connected back to the main vent be sufficient.

3rd question:
Does the toilet vent have to be the same size as the waste water pipe?

4th question:
If another vent is needed for the new toilet location and it needs to be the 3 inch, can there be too much venting if this new 3 inch vent pipe is connected to the original 3 inch vent pipe to avoid having to have another stack vent through the roof?

5th question:
Does the Shower need vented:
Shower will be connected with 2 inch drain to the main 4 inch drain. This shower drain is with 3 feet of the main waste pipe and the main vent is within 2 feet of where the shower drain drops into the main drain?

1st question:
If the main vent is not within this minimum distance can the toilet be vented to the main vent using 2" vent pipe instead of the 3 inch pipe the toilet will be connected to?
Yes
2nd question:
If the main vent distance is questionable for proper venting, could a 2 inch vent to toilet connected back to the main vent be sufficient.
On a 3" drain line you're allowed 6 feet from the trap to the vent. Yes, you could vent at 6 1/2 feet and get by.
3rd question:
Does the toilet vent have to be the same size as the waste water pipe?
No, 2" is the normal size.
4th question:
If another vent is needed for the new toilet location and it needs to be the 3 inch, can there be too much venting if this new 3 inch vent pipe is connected to the original 3 inch vent pipe to avoid having to have another stack vent through the roof?
There can never be too much venting. Your new vent will be 2" and it may revent back into the main vent.
5th question:
Does the Shower need vented:
Shower will be connected with 2 inch drain to the main 4 inch drain. This shower drain is with 3 feet of the main waste pipe and the main vent is within 2 feet of where the shower drain drops into the main drain?
Unless you connect the shower drain to a vented lavatory drain, where it will be wet vented, you will have to run a separate vent for the shower. However, If the shower drain connects upstream from the toilet and is that close to a vent it sounds like you may be wet venting the shower through the main. BUT if the toilet's upstream from the shower the shower will have to be vented separately.
Good luck, Tom