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…

No forced voting in Germany and no Jury Duty (it’s crazy this is even a thing in the US). There are no EU mandates for any of that.
It’s not crazy really, there are good arguments to be made for it. We had it too in Germany until 1924: de.wikipedia.org/wiki/Geschworenengericht
Geschworenengericht – Wikipedia

There’s no jury, but there are Schöffen in Germany. Those are layman judges. If there are not enough volunteers it can be made mandatory for any citizen.
Schöffe (ehrenamtlicher Richter) – Wikipedia