Sometimes there's still a HS mission after the levi died. Right now there's one for Odia M12 at corvus stations.

If I abort a mission I'm not ungrouped and if I was the group leader (which is usually the case after a while) I can take an advanced combat mission and get credited for the adv combat and the aborted HS.

HS don't seem to count towards the mission counter.

After my last mission in odia finished one of the leftover collectors jumped to odia b13 and started mining there instead of pretending to.
I've hit that bot just before it jumped.