Which two types of insurance are there?

The third-party liability and own-damage covers are indemnity insurance: they pay for the actual loss to someone else or to your car. The personal accident cover for occupants that you can add is fixed-sum insurance: it pays a fixed amount for permanent injury or death. So one policy schedule can contain both forms at once.

Not with indemnity insurance. The prohibition on enrichment in Article 7:960 of the Dutch Civil Code stands in the way; insurers divide the loss between themselves under a contribution arrangement. With fixed-sum insurance it is possible: if you take out two personal accident policies, both pay the agreed amount, provided you declared the other policy on the application.

Yes. The Health Insurance Act expressly describes health insurance as indemnity insurance between you and a health insurer. With an in-kind policy the insurer pays not in money but in care, purchased from contracted providers. With a reimbursement policy you are paid the costs. In both cases a statutory compulsory excess applies.

That only happens with fixed-sum insurance linked to a person, such as term life, personal accident or disability insurance. The insurer then assesses the risk and can impose an exclusion or a premium loading. Incorrect answers fall under the duty of disclosure in Article 7:928 of the Dutch Civil Code and can cost you the payment later.