1. Dear *****, your mother has no automatic entitlement to any share in your father's estate. Essentially, the terms of the will govern and it is the three sons who will share the estate of your late father. A wife has no automatic entitlement to any share in her husband's estate. Your mother could potentially take an action under the 1975 Inheritance (Rights of Dependents) Act claiming that she was a "dependent" of your father and seek to get a court to give her a share. However, given the facts you outline where she has lived with her partner for 40 years, this claim would not succeed.
2. I would advise the executor to the will to see a solicitor and to take out a grant of Probate to the will and to proceed to administer the estate and to divide it out between the three sons. This should be done as soon as you can.
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4. Dear *****, if your mother is on the deeds to your father's house, then that means she owns half of the house. However, it does not change the situation in relation to the will. However, you should check the deeds to see what the actual situation is, as it is important to know whether the house is held as a joint tenancy or as tenants in common. If it is a joint tenancy, your mother would inherit the other half of the house. So, it is essential to check this point.
5. You are welcome.