I think Crash getting in would be due to demand, not the heights reached by his series, nor his (tenuous) connection to Nintendo. Third-parties aren't really included on that latter basis. It's just that having a connection can lend them demand, and that demand can get them included.
That's how Sonic, and Mega Man and Banjo did it. Because there are plenty of third-parties with some connection to Nintendo. That in an of itself isn't really enough, it needs to be leveraged into popularity. Look at the remaining Rare characters. They have a Nintendo connection, but let's be real, the chance of any of them being fighters is pretty small, as none really have much demand.
No, characters from the same company aren't mutually exclusive, and it seems entirely possible we get multiple Microsoft newcomers, they have a wealth to choose from.
But also, whether they are licensed at the same time or not is probably going to be on a case by case basis. Like, for base, I would agree that, like, Snake and Simon were probably licensed at the same time. But I think, based on how the content was distributed, Cloud and Sephiroth may have also been licensed at the same time, with one just being held. And then, even though they were in the same wave, I think Sephiroth and Sora were not licensed at the same time (I know Disney owns the license, but Square was obviously involved). You also have to wonder if a character like Bayonetta was licensed for both Smash 4 DLC and Ultimate simultaneously.
I think some characters are licensed further in advance of when they show than others, and also that they will be licensed in waves, potentially returning to the same companies later on. I think it's pretty highly variable, and maybe Crash would be licensed at the same time as Banjo and Steve... or maybe it'd be much later. It depends on the rollout and the unique deals between the companies. There's no one pattern, imo.
Also I agree MS probably will be amenable to cooperation, but of that list only Banjo and Steve were (probably) involving MS. Cuphead the IP isn't owned by them, and Vault Boy, Dovahkiin and Doom Slayer were, I would guess, licensed at the same time, prior to the Bethesda buyout.