I am so sorry you are having to go through this. I had a one year old daughter when my dad was diagnosed and I know how exhausting it can be trying to be there for everyone. Please take care of yourself and remember you have a family that needs you so you have to keep yourself strong for everyone!
I am not sure of any grants. I know that your dad is eligible for social security disability and it starts paying 6 months after diagnosis and it's a fast tracked claim or at lease it was in 2007 when we applied for my dad.
I believe there is something through medicaid where they pay you to take care of your dad instead of him having to go into a facility but I've only vaguely heard of that and don't know if it actually exists or what it requires. I know there is also help through drug companies to pay for his medications and your local charities such as United Way might be able to help. Maybe if he gets the help then your parents could help with your finances?
Hang in there, the future is uncertain but when everything is over you'll have your memories and knowledge that you did all you could for your dad.