You can get the land certificate from land register online for about �3. This will tell you whether his name is on the deeds as one of the owners. It will also tell you whether there are any mortgages or secured loans on the property.
Has your father's estate been wound up yet, & probate obtained? Do you know who he left his share of the house to, if it was owned as a tenancy in common? (If it was a joint tenancy then his share will have gone to his widow automatically, regardless of his will.)
Unless he is an owner, your brother cannot use the house as security for a loan. The fact that he lives there is irrelevant. He is no different from anyone who rents accommodation. However, he could get your mother to sign an agreement - but the loan would have to be in her name - or possibly in joint names of him & her.
If he gets her to sign as a guarantor that does not secure the loan on the house, but it does mean that if he defaults the lender can pursue your mother & eventually get the loan secured through Court action. The house is then at risk of having to be sold if the debt is not paid.
The question of whether such a signature would stand up in Court is a very difficult one - it might depend on evidence of her mental capacity at the time she signed & whether she was put under undue influence by him. Also, the steps the lender had taken to ensure she was independently advised might come into it.