Do Iraq and/or North Korea belong to the UN? And, if not, how can the UN impose anything on these countries? (Also, does the UN periodically inspect other countries which may threaten the pre- 9/11/01 level of world peace, or something like it?)
I can answer the membership question. According to the list of United Nations members, Iraq has been a member since December 1945, while the two Koreas show 1991 membership.
Thanks, IceWolf…very interesting.
Keep warm! 
- Jinx
Hopefully someone comes along with a good answer for the other part of your question, Jinx. Thanks for the “keep warm” – I’ll remember that for winter! 
Why assume that a country has to be a UN member before international law can be enforced upon it?
The Korean War was fought under UN auspices at a time when neither of the Korean states was a UN member. Aggressive use of force by a state is illegal, and can be resisted, and the UN can organise that resistance, regardless of whether the state concerned or the victim state are members of the UN or any other organisation.
No. That is not the role of the UN.
There are UN inspectors in Iraq only because Iraq accepted a Security Council resolution providing for inspectors. That resolution was brought before the Security Council following the (illegal) invasion of Kuwait by Iraq, and was accepted by Iraq as part of the ceasefire arrangements in the first Gulf War. Had Iraq never invaded Kuwait, or never accepted the Security Council resolution, there would be no inspections.
No such resolution regarding North Korea or other states has been brought before the Security Council, adopted by it or accepted by the states concerned.
There are arrangements for the inspection of nuclear facilities through the International Atomic Energy Agency, but I do not know what the scope of these arrangements is, or whether North Korea participates in the IAEA.