I have no experience of how they deal with separations but this must come up frequently. I always found the F/D office very helpful with queries. To ensure your application is dealt with ASAP, phone and enquire before you complete and send in the application.
Regarding the house that they jointly own, your dad will only be assessed on half its value.
Your dad is in care now but not yet under F/D. Bear in mind, if the house is sold before he is in under F/D he will be assessed on half the house sale proceeds indefinitely.
If the house is sold when he is in under F/D he will only be assessed on half the proceeds for 3 years.