Astarion is constantly dissapproving of me - really constantly. But he is still in the neutral range. I don't think, it is possible to get a companion so low in approval, that they leave? Probably with the exception of Wyll, who - as I read here, never did that - will leave when you side with the goblins.
No you can, but it's really very difficult. You need to literally play against him and take every opportunity to do so.
Literally play against him and take every opoortunity to do so? So just play normally and help people?

I'm doing that already - playing a very helpful and nice person and he disapproves literally everything I do and say. He is still neutral. I guess, it's like Nyloth said, it's really hard in teh short span of EA to really piss the companions off. Maybe tehre are a few thing, I haven't done so far, that might do it.