Does research affect abilities like Phase Missile Swarm?

I believe that research affecting phase missiles would - i.e. the better the research, the more of the swarm would bypass the shields...

Yes, you can research abilities that increase a weapons traits. So phase missiles have a better chance of bypassing shields.

In this case, Phase Missile Swarm is just a name. The ability is a generic "DoDamage". It doesn't actually shoot phase missiles, so it's not affected by phase missile research.

Damn I was kind of hoping that it was.  Thanks.

What about something like explosive nanites? Does the 30% damage apply to the phase missile swarm?

Yes, it should