1. The claim is made against the policyholder, but your wife will be recorded as the driver

2. You are obliged to report 'all claims and losses' so you should have advised them.  However you can settle it yourself direct if both parties agree

3. Your wife was involved in a fault accident.  The other parties insurance company are entitled to use the provided details to identify your insurer.

4. They can be guided by you, but the decision as to whether to pay out or not is theirs.  Remember, they are in business to make money, so they will not pay out more than they have to. (After all they are paying the repairer, not the other insurance company)

5. See 4. above 

6. Pre-existing damage is excluded from any assessment, but you have a responsibility to pay to put the damage caused right.  With bumpers, this often means a replacement, and a new one at that as bumpers are designed to take the damage in order that the rest of the car doesnt.  The fact that there was already scratches on the bumper does not preclude this.

Overall you have my sympathies, because the only one actually benefits from this kind of claim is the repairer (the other driver has probably found a friend to provide an inflated quote) - and we all end up paying more in premiums because of it