Q. 4) Is there a mitzva to vote in the elections of the country one resides?

A. See question 561 in this forum:
Is there a halakhic obligation to vote in the elections for the various levels of government of Canada? A. It is quite common in times of elections, specially in Israel for the Gedolim or recognized community leaders to voice their Halachic opinion as to the obligation to vote for a certain candidate or party. However, this obligation belongs to the realm of promoting the observance of the mitzvos of the Torah, not as a required mitzvah per se. (Much has been written about the permissibility of joining Israeli elections. See Hilchos Medinah ch. 3, from Horav E. Y. Waldenberg Zt”l, Horav Nissim Karelitz Shlit’a explaining the Chazon Ish position – Vezorach Hashemesh p. 408, Vehoemes Eid Leatzmo 13, et. al.) In countries where vote is compulsory (and often enforced,) as in most of Latin- America, Australia, Greece etc., voting would be a Halachic obligation based on “Dinah D’malchusah” or the obligation to comply with the law of the land. (Nedorim 28a, Bava Kama 113b etc. Shulchan Aruch C.M. 369: 8). In Canada, to vote is a right and not obligatory (Section 3 of the Charter of Rights and Freedoms). Yet the Novi Yermiyahu (29: 5-7) encouraged the Babylonian exiles to “Build houses and dwell [therein], and plant gardens and eat their produce. – And seek the peace of the city where I (Hashem) have exiled you and pray for it -, for in its peace you shall have peace.” Certainly a successful and truthful democracy is essential for peace. Horav Shlomo Miller’s Shlit”a opinion is that indeed exercising our right to vote is advisable and recommended, but not obligatory.

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