Can a doctor dismiss a patient from his practice if she refuses to believe something well-proven that relates to his field?

Yes they can

Just like a patient can stop seeing a Dr because they don't like his advice a Dr can refuse to see a patient who doesn't follow their advice

Again, YES

a doctor can dismiss a patient for anything that is not illegal discrimination (ie based on race, religion, etc).

i recently had an alleged doctor dismiss me because I am low income due to being severely disabled and can't afford to pay for physical therapy, that I can actually do on  my own for free at home.   He insisted I had to pay someone to do PT by phone with me.  I've done PT about 4 times in the past, it was only a waste of time and money....all things I can do on my own for free.

I don't believe you have to pay for PT for it to be effective...he insists you do.

Yes, for causing disturbance and not following orders. Also called non-compliance. 

Why would someone continue to see a doctor if they don't want to follow his instructions and advice or take the medications he prescribes?

But yes, a doctor can refuse to see patients who refuse treatment.

yes.  doctor has the right to refuse to treat patients who do not or will not follow advice.