This is nonsense. Most/all democracies have laws that only certified doctors can practice medicine. This makes doctors unequal from other people. Is this incompatible with democracy?
Freedom is not absolute because your freedom stops where somebodys freedom beginns.
Hence, if you practice medicine without qualifications there is a high chance you will hurt somebody. It is not undemocratic to protect against hurting others. Hurting others is not a right.
Interesting thought exercise though.
Yes. This is why every society of note limited the franchise prior to the 1900s. You can only have debates among equals among people who are equal. The sort of equality communists imagine requires that you either radically re-engineer the human pysche or implement Harrison-Bergeron-style handicaps on exceptional people.