So, if the speculation is correct that there is a large Neptune sized planet way out there, how would it have formed?
Could it be a captured isolated planet? A planet that formed in the Solar System but somehow got ejected?
It’s the Death Star. 
With the demotion of Pluto, wouldn’t that be Planet IX?
I don’t know if you’re making a joke, but of course the term is in reference to the letter X and not the Roman numeral.
Anyway, as to the OP’s question, I think the null hypothesis would be that it formed at the same time and in the same general way as the rest of the solar system, unless there was evidence for thinking otherwise. I also don’t know what you mean by it “somehow got ejected” from the solar system. It’s still well within the solar system (if it exists). Our solar system is much bigger than most people realize - the distance from the sun to Pluto is only about 1/50,000th of it. There’s a ton of room out there for other stuff we haven’t found yet.
Suppose we had a neptune/uranus type planet ejected from it’s orbit…what size would it be when all the various gasses freeze to ice?
That’s almost surely what it is. Whe should be able to send up small group of f 15’s to take it down.
If it was “ejected” it would surely have a highly elliptical orbit.
There’s nothing out there to suggest it could form by accretion in situ,
so it would have to be captured. This would only occur if it the speed, relative to the sun, was just right, there being nothing out there to alter the speed… See, too slow, and it falls in to the sun, too fast and its not in orbit, it just keeps on going…
What chance that is is the remains of a companion star?
At first, yes, but such an orbit could be modified subsequent to “ejection”. Ejection from the closer-in parts of the Solar System is, by far, the most likely way it could get there.
This definitely didn’t happen. There wasn’t enough gas and dust that far out during the formation of the Solar System.
Nope, couldn’t happen, at least not that way. You need some third object to carry away excess energy. It is possible there was a third object and it was captured, but very very unlikely
Zero. Its projected mass is way too low for that. Also, stellar remains (white dwarfs and neutron stars) are warm enough that any that close would have been discovered years ago.
This hypothetical is addressed in the article on Planet X in this month’s Scientific American. Apparently if it was ejected early enough in the formation of the Solar System (in the first 10 million years) then the remaining dust in the primordial disk could have circularized it’s orbit.
If it is in the plane of the ecliptic, doesn’t that pretty much necessitate its formation from the primordial disk?
A nitpick, but the proposed planet is not necessarily large but is massive. It could be a rocky super-Earth.