Got some more information.
The K. Rool and Krystal trophies, so far from what I have, are the ONLY trophies from their franchises that CANNOT be placed in one of the display cases. All of the other trophies from their franchises can be displayed in the cases, however. For instance, Krystal does NOT appear in the Star Fox: Assault display case. No idea why. Could be that her trophy description doesn't limit her appearance subcategory to "assault" alone, like the Assault Fox and Falco trophies. Instead, it includes that she has appeared in Adventures (but there's obviously no Adventures display case). However, her trophy is essentially the exact same as it was on the 3DS version, where it looked like her appearance in Assault. Very strange...
I have no idea if more display cases can be unlocked. I have 81 display cases. The maximum number of trophies that can appear in a display case is 8. Not all display cases have 8 trophy spots. Some have 7. There are two rows of trophies. If a display case has 8 trophies, there are 4 on the front row and 4 on the back. If a display case has 7 trophies, there are 3 on the front row and 4 on the back.
It can be noted that there are some other trophies that cannot appear in any of my current display cases--most of them were unlocked through the challenges, like K. Rool and Krystal.
Dang it Sakurai! I wanted to enjoy these trophies the way you said we could, by viewing them in the display cases like a collector! I can't do that though, and I have no idea why they can't be shown in the display cases...
As for Star Fox-centric display cases, there are three, according to what I have so far:
"Star Wolf", "Star Fox: Assault", and "Star Fox".
Fox and Falco's fighter trophies appear in the "Star Fox" display case. The "Star Fox" display case has spots for 7 total trophies, not the maximum 8 that most have.
Here's another thing that's strange about the "Star Fox" display case:
It doesn't follow the 7-trophy normal allotment per row.
Instead, the "Star Fox" display case has
4 trophy spots on the front row and
3 on the back. No other 7-trophy display case, of the 81 display cases I have, do this (they all follow the normal pattern I pointed out above). To be honest, it looks awkward compared to the rest...
Just an interesting little detail I noticed on Lylat Cruise's Final Destination mode. In the background you can see The Great Fox, 2 Wolfens, and 1 Arwing. Panther and Leon are presumably in the Wolfens and Slippy is presumably in the Arwing, and Peppy's in the Great Fox, and Fox and Falco are fighting, so where are Wolf and Krystal?
I just confirmed that the Lylat Cruise stage does indeed change background depending if it is Omega or not:
With Omega: 1 Arwing, 2 Wolfens.
WITHOUT Omega: (at least) 2 Arwings, 3 Wolfen.
On the other hand, the Orbital Gate stage has the same number of Arwings with
or without Omega form (3).