Questions whether the President’s Twittering implicates our First and Fifth Amendment Rights

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An op-ed in the Washington Post today ( 6-7-2017, https://www.washingtonpost.com/posteverything/wp/2017/06/07/president-trump-is-violating-my-constitutional-rights-by-blocking-me-on-twitter/ ) came from a person blocked from the President’s twitter account. Because the President concedes that his (now government) Twitter account is his preferred method of communication with his constituents, this op-ed raises an intriguing set of constitutional questions:

(1) does blocking those constituents from a government communications channel abridge the First Amendment right to petition for redress of grievances?

(2) even if certain constituent communications would otherwise justify blocking this channel of petition, is there a Fifth Amendment right to due process (notice and a hearing before a neutral arbiter) before being blocked from these government communications?

(3) is there a Fifth Amendment equal protection denial by allowing some but not all constituents access to a government agent (the President) through this mode of communication?

All of this is besides the open records/archiving question: how is the President assuring that these official communications are being properly preserved?