Non-0K missions legal?

Looking at the single-player missions, a good part of them are for non-0K games I don't have; however, these still work for me and act like they are from that game. Is this legal?

Missions made for BA/XTA/NOTA are probably breaching IP rights of Atari - current holder of TA rights.
They should not be visible to you unless you disable limited mode of zero-k lobby. They should not be visible on the site either. Unless you do http://zero-k.info/Missions?zk_limited=0

Is that OK?

Technically, you can only use TA content if you own a legal copy of TA. The games (BA, CA, XTA, NOTA, BOTA) contain at least some original TA content. The missions designed for TA-based games may or may not contain TA content... I'd guessing that you're okay playing the missions.

There are currently no other legal concerns.