If you bumped into a friend's car and there was no damage but the police wrote you a ticket for careless driving what will happen with your insurance?

Depends on the kind of insurance you have. There are two types of insurance - mutual and standard. Mutual is a kind where your premium changes based on your claims. Tickets and other minor violations doesnt affect it much. On the other hand if you have a standard insurance, the premium might change for every violation reported as well as any claims.