The insurance company is the one that determines fault so if you deny it, they can still rule against you.
Ask a lawyer about it.
a judge in an American court makes the decision as to who is at fault for an auto accident. some states have "no fault" meaning in an accident all parties involved are given a percentage of the accident's fault
each contributes 50% to liability or fault.
No, you have to pay your deductible.
That depends on the nature of the accident, types of insurance coverage you possess, and whether or not you are at fault.
If there is no fault, then by definition there is no negligent party - negligence implies fault.
Yes, The at fault party is responsible.
You should file an Auto Accident report with your local authorities, this is a standard procedure for any accident whether you are at fault or not. If you have sustained damages or injuries you should also file a loss notice or a claim with the other party's insurer to receive compensation for your loss.
At fault driver
According to http://accident-law.freeadvice.com/auto/fault-no-fault-car-accidents.htm, Texas is one of the states which has some form of no-fault law.
Simply put, it is the at-fault party's responsibility to pay for the damage caused in an accident. If you live in a no-fault state, then you and your insurance company will pay for your own injuries, but the at-fault party is responsible for property damage.