On the title question. We can get rid of Astarion, one of the companions that will be playable in the full release, and just found out that Shadowheart too can be subtracted to the party, so I think there's a way to get rid of every and each companion.
Gotta say this post made me curious so now I want to try runs without recruting this or that companion (can not afford to try to make the character despise my toon enough or the trigger to push them to leave the camp with my playstyle I end up with neutral approval by Lae'zel and Astarion and high approval from Shadowheart, Willy, and highest approval from Gale).
You can get rid of every single one and killing all of them permanently, you can technically play the game solo but good luck with some of the fights. some of the enemies will one shot you.
