Do I have a right to sue/issue death threats to people who critise South Park?

No one has the right to issue death threats to anyone. As for sueing you would have to prove, slander. libel or intent to do bodily harm Speak to a lawyer about what your rights are in this situation, but no death threata, that could land you in jail and if someone killed someone there and you wre overheard making death threats you would certainly be on a list of suspects, guilty or not.