According to most traditional Sunni fiqh, the answer is usually 5 times No because answer 1 is a No.
Also according to Sharia law, punishment according to Sharia is to be executed by the institution of the country. If there is no such institution established in the country, judgement can be made but execution is prohibited.
If the foreign country has empowered a Sharia court to judge over Muslim:
In non-Muslim countries, this is occasionally the case for civil law such as marriage and inheritance but I don't know a non-Muslim country that attributes all judgement for Muslim to a Sharia institution. It is to mention that even many Muslim majority states do not accept Sharia courts in penalty law. So this is only a theoretical exception.
Many countries allow to judge a National of their country to be judged for deeds committed outside the country so that the person may be judged when returning to the country of origin - provided that judgment and penalties according to Sharia are established in this country.
Iranian judges have ordered to execute a Sharia penalty abroad; I don't know whether Shia fiqh can be defined by the authority in place.
In Sunni Islam. mostly self-nominate "judges" have decreed alike.
In both cases, execution of Sharia penalty in a state where this is not permissible is punished by this state as an infraction of law; in this case: as murder.