My Dad has an apt attached to his carport and gets cash every month for this. Can he still apply for Medicaid?

You would need to check with your State Medicaid office to see what rules and regulations they have.... each State is different. Your Dad may or may not qualify depending on what is the income limit.

Can you Dad still afford to live in his home or is it starting to get too expensive for him? Is he able to maintain it, keep it up-to-date with repairs, insurance, property taxes, etc? If it is starting to become a struggle, might be a good time to downsize to something smaller and more manageable. Better to do it now, then later.