If you have an excess on your policy you will have to pay it if you claim. The insurance company may waive it before you pay if they think the case is strong and they will get their money back, or refund it later if they do get the money back from the other guy's insurers. However, they are neither obliged to waive it or reclaim it for you - it is an "uninsured loss". Check your policy terms to be sure as different companies vary.
If your insurers recover everything they pay out they should restore your NCB. Again, as said above, some use the fact that you actually had an accident, albeit non-fault, to raise your premium come renewal. IIRC Admiral rely on stats to say that if you have had a non-fault accident you are more likely to be involved in another accident!
Check your policy to see if you have legal expense cover. You can use this to pay for a claim for any "uninsured losses" you do not recover from your own insurer. You may also have it on your household policy or credit card.
To the guy who suggested it would be a Cat D - I very much doubt it for such minor damage.
HTH.