Certainly nothing wrong with treating everyone who is situated the same equally. That is what the government must do. Private persons and companies, though, do not have that obligation except in limited circumstances where some statute or ordinance requires it. So, for example, all employers with at least 15 employees must not discriminate on the basis of race because a federal statute (the Civil Rights Act of 1964) prohibits employers from doing that. Many states similarly provide by statute that employers may not discriminate on the basis of race. In the absence of those laws the employers would be free to discriminate on the basis of race if they wished.
Not a "higher status." But certainly the rules for what governments may do are different than what private persons and entities may do. The Constitution protects the public against government abuses since without those protections the government, with its police power and military power, could take away cherished rights and mistreat the public. One only need look at China to see that.
No, it is not providing "public services". It is a private firm that provides a platform for people to communicate with each other and stay in touch in a variety of ways and that is supported by selling advertising. And while it is certainly by far the the largest platform providing such services it is not the only one and thus not truly a monopoly.
No. It has no legal mandate to provide any particular service, let alone whatever you mean by "comprehensive services". It is private firm and gets to decide what services, if any, it will provide to customers.
As already discussed, the Constitution's protection of Free Speech only protects you against government interference with your speech. It does not require any private person to provide you a platform for your speech, does not require private persons to be neutral or balanced in the views they present, nor otherwise regulate private speech. Indeed, the Constitution's protection for free speech means that Facebook too may say what it wants and express whatever views it wants. This means that if Facebook wanted to present pro-China views, it is allowed to do just that. The government cannot prohibit Facebook from doing that because that would infringe on Facebook's free speech rights.