Yes, and this is true in virtually every country. The licenses of almost every country are accepted for visitors in any of those same countries, thanks to some UN conventions.
An international driving permit which uses a standardized format and includes translations may be required.
Not true in many EU countries. In France you're supposed to get a French driving license after two years of residence. Never heard of this being enforced, but I know people that changed when their licensed needed renewal so they could deal with a local administration.
This is not compulsory. It is perfectly legal to keep your EU/EEA licence as long as it is valid. They can force you to exchange it for a local one, though, if you commit certain driving offences.
It is required to get one in your country of residence when it expires (and licenses that are valid for life can be limited to two years), or if it is lost, stolen, or damaged. That's not what I would consider "without time limits," and certainly not what I would consider "as valid" as a local Norwegian license. It's more of an extension of the several months or year that people from any other country get.
An international driving permit which uses a standardized format and includes translations may be required.