I do not see anything that would impact your travel plans with the limited facts you posed in your question. If you have an attorney, then of course, keep them informed of your dates out of the country.
This can be extremely difficult to prove. Renewing by a phone call without payment is highly unlikely. Any and all evidence you can think of to help you prove this would be reviewed by your insurance company to see if they can make an informed insurance coverage decision.
I fully agree with the other posters on your questions and concerns. Just remember, it depends on the injuries of the other party: was there surgery, is there a permanent medical impairment to any particular body part as a result of this accident. Those are the real value drivers on a personal injury case (to raise value). There is a possibility that your case will settle in mediation too: statistically only about 5% of personal injury claims actual go all the way to trial. Definitely...
It depends. The burden of proof will rest with the District Attorney or prosecuting attorney to "prove" you were in operation of the vehicle while under the influence of alcohol. It certainly does not help that you were intoxicated at the same time the vehicle was found; absent any further proof from the third party actually driving your car (witnesses) it may be a difficult case for your position. Definitely consult with an experienced criminal lawyer for further review.
You should review this with a personal injury attorney:
You need to review liability on the chair being defective and balance this with your daughter's injuries. Much more information is needed and you need to be careful with a skull fracture injury. Skull/brain traumas are a huge responsibility. Without an experienced lawyer, you will very well miss other damages that may or may not be related to this injury claim.
Yes, you are responsible for this bill. Due to the fact the car you were in rolled back causing damage to the other vehicle and the need for the other party to employ a rental agency. It should only be for the time the car was being repaired and a day for them to return rental after being notified the car has been repaired.
I need more information. Based on this you should contact an experienced Medical Malpractice Attorney; however, not withstanding this, if your doctor did deviate from the standard of medical care that also caused you injury, then you may have a claim for Medical Malpractice. Also, if it is within the reasonable realm of medical probability, and you consented to this in writing (see your informed consent form you signed with doctor and surgery center), then you may have no claim. More...