My family put my father out of their home. My father requested me to take care of him. Family believe I shouldn't use his funds but use mine.

Whatever you do make sure you keep copies of all receipts! This will become a nightmare if you don't.

Why is it their business? They kicked him out, so they are out of the picture. You don't need to show them the bills, how it's spent etc. They relieved themselves of the sponsibility.
You don't need to answer to them. I agree with gladimhere. Spot on!
Who is power of attorney?

Your father was living with another family member and got kicked out. Why? What did he do? Does he need to go to a doctor? Does he have issues with his brain? Finding out why Dad got kicked out of where he was staying is your #1 priority. You need to know if it’s safe for him and you for him to be living in your house with you. Do you work? Is Dad alone during the day? Is he safe being alone?

He uses his debit card for you to take care of by calling who?

Yes, he should pay as much as he can for his care. And you do need to make a legal paper saying he is paying you for it. Attorneys will often give you a free hour to talk to them about what you need.

He was kicked out of his home? Yes, you should use his resources for his needs. Get a rental and caregiver agreement so he will pay a portion of household expenses and for care you provide.

See an elder law attorney for assistance. Yes dad should pay for attorney also. Does he have powers of attorney, etc in place?