Like most places , death penalty is for capital crimes basically , and rape is considered a capital crime also. The method of execution in Yemen is hanging.
However one must also take into account Yemen has been unstable politically for some time , and a war with anti-government rebels still rages on. So not everything is done by the book , the situation in some parts is like martial law (that means a ruling of a military court judge will over rule others), and in some other parts , like east of the country , life is very normal.
You did not provide any support for your claim that speech against Islam in Yemen is punishable by death , what is the legal article ?
Also , about the case of Raja Hakimi , you omitted the following part of the case:
"Abdulrakeb Alhimyari, the deputy general director of legal affairs in Ibb, told Al Arabiya English that killing was ‘possibly planned beforehand’."
The appeals court found evidence the murder was pre-meditated , and over ruled the original 2-year prison sentence of first instance court where she was claiming self defense. In other words the court found it was a set-up & pre-planned to claim self defense. There is a difference between self defense , and making a planned murder look like self defense.