You can reduce payments by offering a voluntary excess, but keep in mind not to offer a huge sum as you will need to meet it if you make a claim that is your fault. many think they will never make a mistake and it will only be someone else, but statistics shows otherwise.
If you're involved in a road traffic accident that isn't your fault you have the right to claim back losses from the responsible party. This should not impact your no claims bounus as it was not your fault.
A fully comprehensive car insurance policy will cover any personal injuries to third parties including your passengers as well as your car and theirs, in the case of the accident being your fault, or no balme to either side.