No, you don't.
Yes, they are. But the policies and platform of the service provider take precedence.
They don't have to allow or disallow anything because you don't have a right to free speech on a private platform. Period.
Not relevant.
The difference you're failing to grasp is that the policies of the service provider take precedence. If the company wants to allow anyone to block anyone, they can. No one, regardless of status, can "violate" someone's freedom of speech if that provider does not guarantee it. That's how that actually works.
Irrelevant.
Neither governments nor courts can dictate what is or isn't a "public forum" on private servers. This right is exclusive to the service provider/owner.
Also irrelevant.
As far as those links go, it seems even courts don't understand how the Constitution works. Since we're posting links, though:
http://www.washingtonexaminer.com/no...rticle/2628332
https://www.bloomberg.com/view/artic...locking-tweets
Twitter is not a "public forum". It's a limited-character "blog". It's his account, not the "people's". He can block, delete, etc, all he wants. He can even disable comments altogether, should he choose. People need to learn how the first amendment and words contained within actually work rather than getting bent out of shape over getting blocked because of something stupid they say on a platform for imbeciles.