Q. 2) Is the government of the Torah elected democratically? How?

A. See question 1188. Talmud (Brochos 55a) teaches that “We do not appoint a Parnes or community leader unless the people were first consulted.” Pirkei D’Rabi Eliezer (11) mentions that: “the people choose the king, the king does not choose himself.” Abarbanel (introduction to Shoftim, first part) writes: “Judges and kings are named through Beis Din, but the people have to accept them. Rambam (Peirush Hamishnayos – Bechoros 4:4) rules that the Exilarch (Reish Galussa) can only be appointed with the consent and acceptance of the community.
Rema in Shulchan Aruch (C.M. 163: 1), Hagoos Maimonios (H. Tefila 11: 2) and others rule that all tax paying individuals should be summoned to voice their opinion and the majority will decide. Avnei Nezer (Y.D. 312: 5) and others explain how majority rules. Chazon Ish (Baba Bassra 15a) describes an advisable method to be used in a large city. Namely, to choose representatives from every congregation who in turn will elect the Seven Leaders or Tovei Hair.
Horav Shlomo Miller Shlit’a mentioned the opinion of most Poskim that the people are granted a vote when they pay the community taxes.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a