The wire that is used for connecting the ground rod or plate to the electrical distribution is governed by the size of the electriclal distribution. In Canada a #6 bare copper is the minimum size for a 200 amp service.
Conductor sizing is based on the amperage that the service is rated for. Common size services are 100 and 200 amps. The conductors would be #3 copper and 3/0 copper respectively.
A #1 copper conductor with an insulation rating of 90 degrees C is rated at 145 amps.
This can't be answered without knowing the voltage, and ground is not the same as neutral, in AC circuits, which I'm assuming this is.
A conductor used for grounding of the main service should be a single wire. The code book has a table that states the size of ground wire for different service panel amperages.
From the question it is hard to establish whether the service size is 350 amps or the service conductors are 350 MCM in parallel. If the service is 350 amps, the grounding conductor is #3 bare copper wire. Parallel 350 MCM conductors will allow for a 600 amp service. The grounding conductor for a 600 amp service is a #1 bare copper wire.
#2
A #1 copper conductor with an insulation rating of 90 degrees C is rated at 145 amps.
This answer is taken from the CEC. Table 17 states minimum size of grounding conductors. For a service conductor drawing 400 amps a #3 copper grounding conductor is needed. Also see rules 10-206, 10-700 and 10-812 if you have access to the code book.
A 100 amp residential service requires a size #8 copper wire, it should be insulated in green.
This can't be answered without knowing the voltage, and ground is not the same as neutral, in AC circuits, which I'm assuming this is.
Answer for USA, Canada and countries running a 60 Hertz supply service.CEC states that a #3 bare copper conductor is a common grounding conductor size for a 200 amp service panel and it is the minium size for service raceway and service equipment of 400 amps.
On large service entrance services the neutral can be reduced. The amperage of the service and the voltage of the service and the insulation factor of the 500 MCM conductors need to be stated to answer this question correctly.
The minimum size wire that can be paralleled together stated in the electrical code book is a #3 copper conductor.
Notes: 1. Where multiple sets of service-entrance conductors are used as permitted in Section 230-40, Exception No. 2, the equivalent size of the largest service-entrance conductor shall be determined by the largest sum of the areas of the corresponding conductors of each set. 2. Where there are no service-entrance conductors, the grounding electrode conductor size shall be determined by the equivalent size of the largest service-entrance conductor required for the load to be served. 1 This table also applies to the derived conductors of separately derived ac systems. 2 See installation restrictions in Section 250-64(a).
For service sizes of 100 amps and less a #8 bare copper conductor is required.
2 AWG Aluminum.
250 mcm
A #6 copper ground conductor would be needed.