You may be correct on 1), but take a look at http://en.wikipedia.org/wiki/Brandenburg_v._Ohio There are a few tests that have to be met. The key piece is "The Court held that government cannot punish inflammatory speech unless that speech is directed to inciting, and is likely to incite, imminent lawless action."
On point 2), I still think there is a clear difference in kind between government and private entity bans. The government can enforce their bans with legal threat of violence (i.e. You can go to prison). Another point of distinction is that within private spaces there may be implicit endorsement by the private space owner. For instance you have the public right to promote a political candidate, but if you do it by planting a sign on my lawn, it is implied that I endorse that candidate. I may not want to make that endorsement and restrict you from posting your sign, but that is not nearly the same as the government saying "No one may publish endorsements for Communist Party members".
On point 2), I still think there is a clear difference in kind between government and private entity bans. The government can enforce their bans with legal threat of violence (i.e. You can go to prison). Another point of distinction is that within private spaces there may be implicit endorsement by the private space owner. For instance you have the public right to promote a political candidate, but if you do it by planting a sign on my lawn, it is implied that I endorse that candidate. I may not want to make that endorsement and restrict you from posting your sign, but that is not nearly the same as the government saying "No one may publish endorsements for Communist Party members".