As for war crimes, article one states: ""settle any international disputes in which they may be involved by peaceful means in such a manner that international peace and security, and justice, are not endangered, and to refrain in their international relations from the threat or use of force in any manner inconsistent with the purposes of the United Nations."

So only so much as war crimes are inconsistent with the UN. In short, probably do care. But only as much as "refrain".

As for the second question: no. Can't join if at war. Why tho? I can't find a clear answer. The arguments range from: no, because that put article 5 in conflict with article 1. No, because then that means war with Russia and nobody wants that. No, because the process to join NATO requires political, economic and military integration that cannot occur while a country is at war.

Eh, I'm not convinced by some of those.