Can I sue him ??

Yes but that is probably not the best way to handle the situation.

Would these remarks qualify as intentional slander?

I don't think they would. Those remarks were simply his interpretation of your actions. You might want to consult an employment attorney.

In theory yes. Consult an attorney in your area with the specifics.

Would Party 2 be able to sign on Party 1’s behalf in developing a new Durable POA document designating Party 3 as Durable POA?

Consult a local elder law attorney. It appears from your question that the documents allow for that but you really need an expert in this area to...

As blackmail is illegal, what happens if they reveal the information about me during or even after being convicted?

Consult with an New Mexico Criminal defense attorney. You may also have a civil remedy but I would start there.

Is hit and run great-granny guilty or taking the rap for someone?

You might want to get her an attorney who handles traffic cases.

Would my business or personal insurance be liable to defend me?

You will likely be covered. Report this to your insurance and cooperate under the terms of your policy.

What if I have no insurance but the other driver is at fault for an accident?

If you were injured call a personal injury attorney.

I'm looking for advice for a malpractice case. My mother needs 24/7 care for a surgery that should of been an "easy fix."

Get the records and have them reviewed as soon as possible. That is the only way to know.

How much money can I sue this doctor for and what are the chances I will get the money?

You can sue him for whatever you like but your chances of recovering anything are low. Have your records reviewed to be sure.