In terms of involvement. Not direct combat. There's a pact between UK, Australia, USA and NZ that is one's attacked, they have to join in. So yes, NZ would most likely have to send some troops over, declare war, etc. to some degree or another
It's based on EU commitment. If one are attacked, everybody has to go in. But otherwise no, they'd probably only send money, equipment and maybe some volunteer troops to the warzones
Stop making disinformation. It's not an EU directive, it's NATO. Not all European countries are members of NATO (like Switzerland or Austria for example). So in an hypothetical war even minor countries like Montenegro and Luxembourg have a duty to go war and you didn't mention them in your quiz
You too are spreading misinformation. Montenegro isn't involved with the EU. The EU isn't the entirety of European countries, it's a political and economical union consisting of 27 countries.
First comment on this Quiz -Aug 5 2021
aside that, Great quiz!!!