Are both of these things mandatory for EU citizens?

I'm mainly talking about: - Voting (at federal elections) - Jury Duty (at a courtroom) I know that in certain countries like Australia f…

Speaking for germany: no mandatory voting, no jury duty.

Being part of a jury is voluntary and you have to apply for it. It’s also probably quite different from the US jury system.

There is a form of jury duty in Germany: Schöffe (honory judge).