Will Medicare or Medicaid pay Dad's bills if I take him to see a doctor or cardiologist outside Hospice?

No one can put a timeline on when someone will pass away. I’ve read on this site that some people have been released from hospice care. I don’t see why you would not be able to take him to his doctor, but before you take him to a specialist, I would see if you need a referral. You can also speak with the hospice workers. 

There isn't an "exact timeline" on hospice. No one can say exactly when someone will die. My husband died after 5 weeks on hospice. The hospice nurse was very surprised -- she had expected another month or so. My mother was on hospice care 3 months when the service was discontinued, because she had improved so much. She lived another 2 years.

Discuss your concerns and questions with the hospice nurse. Read their literature.

To take dad to outside doctors you need to cancel hospice first. You can reinstate it again later if that seems appropriate. Again, discuss this with the hospice nurse.