How does the new law affect the bonus system of insurance companies?

The new Act governing motor liability insurance does not oblige companies to change their bonus systems. On the other hand, the law enables more flexible utilisation of claims histories.

Claims history data are specific to each individual policyholder. Does this mean that, should an accident occur with one vehicle, this will also have effect on the bonuses of the policyholder's other vehicles?

Not necessarily. It depends of the insurance terms and conditions of the company concerned. Check with your own insurance company.