I will soon have in my personal possession a second starport. It's on a different planet, I'm wondering if I can link these together for NPC transport travel and if so what would I need to tweak to make this so?

I believe they need to be assigned to the same transport faction (I don't think they have to be owned by them, but you never know). It should then be good to go except you will have a list of all their starports, not just yours.

Just have been as manager is enough. No ownership is required.

So lemme get this straight...
Assign a Transport Faction as Manager
Assign Facility Operator (preferably lvl 5) as Operator

How does one collect FI on a Starport?

Fi likely goes to the managing company similar to how casinos and such work.

Well at least I like my Transport faction, and don't mind "Paying" them to afford me a useable Starport. Thanks!

Or you could simply come to an arrangement with the managing faction to have them send your starport FI to you every month. Messi, I'd suggest you have a chat with SYT as I think they already manage a few on one of the planets you're on.