Note that this is not the case everyone in Europe necessarily. But you can cross outside zebra crossing in the UK, Netherlands, Greece, Denmark, Sweden, Finland, and Norway.

In some countries like Italy or France it is legal as long as there's no explicit zebra crossing nearby (e.g. without 50 or 100 meters).

In most of the countries, crossing the equivalent of highways or interstates is illegal (except in designated overpasses and such).

Regarding the question about what happens to drivers, here's an example for what's the case in Belgium "any physical damage to a pedestrian caused by a traffic accident shall be compensated by the insurance of the drivers involved, regardless of the responsibility of the pedestrian, except if that pedestrian is over 14 and wanted the accident and its consequences to occur."

https://en.wikipedia.org/wiki/Jaywalking