I have a Hangar Bay event coming up this weekend, but I've never played such a format, and have questions.

Does the distinct rule mean I can't fly (for example) two TIE swarms with different named pilots?

Can the squads be from different factions? (A Rebel list, and a Scum list)

1) No, it means you can't have the same named pilots & upgrades in both your two lists. So if you have Howlrunner in one list, you can't have her in the other. If you have Lone Wolf in one list, you can't have it in the other.

2) Generally yes, but local events sometimes play around with this so best to double check with your TO/judge ahead of time.

1. As long as the squads don't share the same unique pilot/upgrade card it is fine
2. Yes you don't have to have 2 lists of the same faction or 2 different factions

There is a variants (might have been a similar format before Hanger bay was official) that required you to bring 2 different factions and you always played against a different faction. But official FFG System Opens are much more lenient than that.

Distinct rule meant you coulnd't have ANY of the same things in your list last I checked. So not only not two Howlrunners or not two Vaders (pilot and crew being the same card for this purpose) but also, you could only have PTL in one of the two lists. As many copies as you want in that list, but only in one.