Yes. It happens from time to time. By the way, beside the fact that most european countries won’t extradite someone facing the death penalty, Portugal won’t even extradite people facing a life sentence since it doesn’t exist in this country (the maximal sentence being 30 years, there).
Yes. But there are other cases when France won’t extradite someone :
-More generally than only the death sentence, when the penalty the person is facing doesn’t exist/ is considered barbaric in France (say amputation or forced labor)
- When the person has been tried “in absenstia” (wasn’t present during his trial because he fled or for some other reason) unless he’s guaranteed a new trial.
-When whatever the person is accused of isn’t deemed a crime under french law
-When the person is a french citizen
-When the french courts are competent for the case (when the criminal or the victim is french, or when the crime has been commited on the french territory, mainly)
-Often (but not in all cases, I don’t know the details) when the crime is political
-When the person is a political refugee and the extradition is requested by the country he came from
-Of course when the accused isn’t guaranteed a fair trial
Finally, AFAIK (I’m not absolutely sure), the minister of justice can always refuse an extradition, for any reason, even when the courts allow it.