A.
Yes, you do. Probate is the legal process which allows the executors (or administrators) to be able to finalise and then distribute the estate, and must be applied for after a person dies.
Once granted, a Grant of Probate is used to demonstrate that the executors have permission to carry out their role. For example, the bank where the deceased person held a bank account will require evidence of probate before transferring any funds under the direction of the executor.
The Will is an expression of what the deceased person wishes to happen to their estate. Probate is the legal permission given by the courts allowing the executors to enact these wishes.
Whether or not probate is required to execute the Will, depends on the assets held by the estate. There are exemptions to probate, for example, when a bank account balance is a very low amount.