I'm not sure if this is exactly a BGS question but what does it mean when you find a player faction in a system that has no associated squadron?
Is there some way to track the player group that "owns" the faction?
No-one "owns" a player faction - not even the player group that requested the faction to be created. Since players cannot formally affiliate with or join a minor faction, there is no way in-game to tell if there are any players or player groups supporting a faction. Best you can do is run a Google search and see if anyone out there on the Internet is currently claiming that faction as their own.
Quick and easy novice question or two: what IS a "Player Faction"? How can I create my own "Player Faction"? And, as a bonus, how is it different from a "Squadron" (which is the in-game equivalent to a "Guild/Clan" system)?
Player-made factions, or "PMFs", have a complex process for creation. They have to be requested by "player groups". To be a player group, you need to register with FD and have at least 10 members, so in theory, an individual player isn't supposed to be allowed to start "their own faction".
The player group files a submission to have a player faction created. The name, government type and superpower allegiance of the faction can be selected (though some superpowers disqualify certain government types). You also nominate a home system, but be aware that many systems are disqualified from being nominated - the inhabited galaxy is rapidly running out of free real estate for new factions. Finally, you get to write a one-paragraph story about your faction, which gets formally added to the game in the home star system's description on the galaxy map.
PMFs are added to a star system with only a small amount of influence and no space stations under their control. The players of the player group presumably then get to work supporting that faction, helping them in their battle for dominance over their home star system, then expanding into and conquering other star systems. It's a popular "end-game" activity for players that own all the ships, have bajillions of credits and have seen and done everything else in the game.
The player group that requested the PMF be made does not have any special control over or authority within "their" faction: you can't rename planets or space stations, write missions for your faction members to undertake, or demand that "your faction" declare war on another faction or invade this or that star system. It's all controlled by manipulating the BGS, just like it is for any other faction.
PMFs are only loosely connected with squadrons, in that a squadron can nominate one faction (PMF or non-PMF) they are affiliated with. The squadron's members then get to access a special screen which lists all the star systems that faction is present in and all the assets (space stions etc) the faction controls. Each squadron can only be affiliated with one faction, but you can have more than one squadron per faction, and there's nothing to stop another squadron from affiliating with "your" faction.