Daniela,
The “precise conditions” to which you refer only apply to a din Tora. The secular authorities (Rambam Hilchot Rotzeach 2:4 and Hilchot Melachim 3:6) or an official bet din acting under emergency powers (Shulchan Aruch Choshn Mishpat 2:1) may execute criminals without regard to these procedural rules (see Shemuel Bet 1:10-16).This is necessary when there is disrepect for the law in order to preserve public safety and order (Ran Derasha 11, Maharal Chiddushei Aggadot Makkot 7a). Thus, Rav Moshe rules (Iggerot Moshe Choshen Mishpat 2:68) that if someone takes murder lightly due to his cruelty or there is a general disregard for this heinous crime the authorities are obligated to institute the death penalty.Obviously this should be done as quickly as possible but not so quickly as to chance doing an injustice (Rambam Hilchot Sanhedrin 13:1).
As for maiming bodies of those executed, this is a very severe step which should only be taken in an extreme situation after serious deliberation. However, if the authorities deem necessary it would appear that it is permissible (see Shemuel Alef 18:25-27). It should be recalled that after Eichmann ym”s was executed his body was cremated and the ashes scattered over the Mediterranean Sea in order to prevent his grave from becoming a shrine for his followers.