How should I file a motion to vacate default judgment in Florida from overseas?

Your lawyers cannot appear in a Florida court directly. They need to be admitted to practice here. If one of them is admitted in another US...

Not on a contingency fee contract. The exception is when the lawyer is forced to withdraw because of ethical issues.

I was having a medical test under light sedation. During procedure i was never "under/out), I asked the doctor to stop was held

you are describing a criminal battery. Call the sheriff/police. Grieve the doctors and other professionals.

I filed a motion for summary judgment and I didn't receive a respone/objection.. its been about 30 days

Assuming you are in state court, no response is required. You will only win if the motion is legally sufficient. The other side can respond up to...

Can I sue the department of children and families?

If you mean for damages, it is unlikely. DCF owes you no legal duty. It has immunity.

On a home remodeling contract iif the contractor has pulled a demo permit ready to start can the customer cancel and refund

Yes the customer can cancel the permit. Whether the customer owes the contractor money depends on the contract, and why it is being cancelled.

Can my attorney go after my insurance company in personal injury claim?

Uninsured motorist coverage applies only to motor vehicle cases. There is no analogue for slip and fall cases. of course, your medical insurance is...

Should a 40% fee occur if jury is selected or trial has commenced?

Typically when the Answer is served denying liability -- far far before a trial.

Is it customary that a lawyer make settlement demands/offers without client?

No. It is an ethical violation. But, an attorney can say something like: "if my client would take $X, would your client pay it?"

Can i fire a deadbeat lawyer???

I am sure I answered this already. The answer is the same: It depends on the law of NM and the contract you signed. But you can probably discharge...