Yes to the first question.
If the Torah allows you to decide on secular law when being on jury duty I see no issue.
From the answers I have been getting it seems that is not the case. Then of course they should avoid jury duty. If they can't decide the case on secular law I can't see them ever being picked for jury duty.
This is why I asked you for an example case.
Let's take admissible evidence and testimony as what might probably be the thorniest issue. IINM the Torah is a lot more stringent on what might be acceptable as evidence or testimony. However I am not sure if the Torah sets the same standard for a "trial" of a Jew which is required to take place in front of a Beis Din that rules based on Halacha, and a trial where no Jew is involved and is required to take place in front of a court that follows the law of the land.
One way or the other, the simplest thing to do is to avoid having to deal with a complex and sensitive matter.