1. I don't think so. Not in the "free speech" sense. Twitter owns itself and should be permitted to do as it pleases with its property.
2. I don't think it's okay, but I think a proper response to it lies in the social sphere, not at the end of the government gun.
3. I think this is probably an inevitable outcome for humanity's first swing at social media. It's centralized and so will come under the control of some partisan group or another. I think the behavior will push us inevitably towards more decentralized platforms.
4. I'm not convinced they have power - not power that can't be removed from them by society, anyway. If they misbehave or underperform enough, society will move on. See MySpace.