Is it possible for a monk to be called for jury duty in the U.S.A.? If so, does the Buddhist religion prevent them from taking part int he judicial process, as it involves passing judgment on others? Furthermore, would it be considered an offense for a lay person to be a member of a jury that had to decide on a death penalty case?
There is another question on here about whether or not a buddhist can harm another person https://buddhism.stackexchange.com/a/7767/471 it claims that the buddha said that judicial action wasn't blameworthy. So you could get away with saying that taking part in judicial action was not blameworty, but if it was me, I would have great difficulty in judging whether or not they had actually committed the crime. And it would be upsetting to discover that they were innocent but my vote was for guilty.
How can it happen that one having left home would still have such duty?
Actually, and that is a serious matter, most countries do not let people go fort, is unknown for them. My person does not know how western monks generally manage such, staying citizens and leaving home: how should that work in accordiance with Dhamma-Vinaya?
Furthermore, would it be considered an offense for a lay person to be a member of a jury that had to decide on a death penalty case?
Sure, to the amout of deed, and it's the kamma of killing if agree by thoughts, signs or deeds.
(Note that this is not given for stacks, exchange, trade or entertainment but for release from this wheel)
As a monk one should not involve one self with govement, law and lay peoples activities other than at a spiritual advisory capacity inline with the Dhamma and Vinaya.
So getting onself excused is the best option. There is also a further karmic consiquance if the one gives or endorse a guilty verdict.