I looked up federal death penalty and there are 63 people on federal death row, with 37 people being executed since it started in 1927. I looked at the cases and many of them involved the body being found on federal land or it was very clear that the kidnapping was in one state and the body in another or it was a murder for hire type thing. In one case, the Dru Sjoden case was the case in which the girl was at the shopping mall in ND and they found her body in another state MN. So it looks like when the feds keep jurisdiction it is very clear where the body is in one state and the person lived or kidnapped in another state or federal jxn is otherwise very clear. There's probably alot of cases where it is murky but it does not seem like the feds take jxn unless it is very clear.
So best chance for a death penalty here (assuming follow what appears to be longstanding practices) would be if they find the body in another state or if it's on federal land. In any event, we never know what the Trump DOJ will do (everything seems a surprise these days) so overturning what seems to be longstanding DOJ practice to give almost all cases back to the states may not be something the Trump Justice Dept chooses to do, especially in a case involving a Chinese national. On one hand, I could see them taking jxn for the optics and to get death penalty; on other hand, GOP is very states' rights-oriented so I am not sure they will want to make this a precedent; they will be accused of taking cases away from the states that do not have death penalty. Also, potential crimes like murder or sexual assault may be states only crimes and I don't think they will want to subject family to two separate trials.
Moreover if they start taking away state's choice on death penalty, it would most certainly be challenged in federal courts by people who get the death penalty and they would have a pretty decent argument especially if it was clear that feds only take jxn when the state is not a death penalty state. Justice department can't very well do things "special" here; the whole purpose of justice is to treat like cases alike.
I wonder if there are any criminal lawyers here who think that even the fact that it is in federal court now is odd. I don't know enough about IL courts to offer an opinion on that but if being in federal court even now is odd who knows how this case will be tried.