First of all, welcome to the website. We are here to help answer your questions the best we can. I am glad that you have not already started your application process. The VA does not have a 'look-back clause' like Medicaid does. The VA is only concern about the income and assets from date of claim. Medicaid looks at any assets that the individual had over the past 5 years.
I really recommend that you contact the local 'bar association' and obtain a listing of elder law attorneys in your area. They can help your grandfather to protect some of his assests and to take care of some of his outstanding obligations before filing a claim with the VA. There are certain types of irrevocable trusts and other avenues to address his assets so that it will not work against him when filing his claim.
As far as the location to file his claim, I would recommend using your mailing address and file with the VA Regional Office in Tenn. Florida has such a large veteran's population and they are really slow in processing claims. You can also download the new POA form and represent your grandfather. This will allow you to submit the paperwork for him and also to follow-up on the status of his claim.
If he files before he goes into an assisted living facility he will probably be denied due to the income limit. We are starting to see where the VA is not just looking at the $80,000 asset limitation but also at the veteran's health and life expectancy. This is why he needs to get his assets reduced as much as possible. The elder law attorney will be able to help him do this within the legal limits.
As far as the first question regarding
'do you have a claim with the VA'. They are referring to a 'benefit claim' and not medical care by the VA. They want to know if he is receiving a service-connected compensation benefit or a non-service connected pension. It does not sound like he is.
Some nursing homes and assisted care facilities do work with someone on a local basis to help complete these applications. There are some who will actually pay for any cost associated to completing the application in order to get the veteran to select their facility. There are also state and county veterans service officers that can provide assistance to you and your grandfather. Check this link for the state veterans affairs office and services offered in Tenn.
http://state.tn.us/veteran/You will probably have some frustrating moments but it will be worth the effort. Besides this is a benefit that your grandfather earned and is entitled to it. He is lucky to have you to look after him.
We are here to help you through the system. Please stay in touch and let us know how things work out for you and your grandfather.