I'm just wondering if your Dad filled in the right form. What he needs to complete is a form to claim exemption for your Mum on the grounds of "severe mental impairment". Might he have filled in an application form for Council Tax Benefit by mistake? This is an entirely different thing, & is for people who are on a low income. If he just asked for a form to claim a reduction in Council Tax, someone may have misunderstood & thought he wanted to claim benefit, which many pensioners are entitled to.
As Pauline says, the correct form is quite short & simple. Part of it has to be completed & signed by the person's GP. A Council Tax Benefit form would be quite lengthy, with lots of questions about income, savings etc.
Basically, if an exemption is granted for someone on the grounds of "severe mental impairment", it means they are disregarded as an occupant of the property for Council Tax purposes. So if there is another person in the house (in this case, your Dad) they are treated as the sole occupant & receive the 25% "single person discount" which is awarded to anyone who is a sole adult occupant. If a person who has been awarded an exemption lives alone, they do not have to pay any Council Tax at all, as there is no-one living in the property who can be treated as liable to pay it.
Hope that helps!