What is the ruling on belittling "sarsagiyyah" and acting arrogantly towards them, and is it permissible to kill them due to their bad deeds even though their sins do not warrant death? And how should one deal with them?

Those who commit crimes need a savior from misguidance, one who calls them to Allah, advises them, enjoins them to good, and forbids them from evil. If they do not respond, then it is incumbent upon the ruler to punish them. As for individual people, it is not permissible for them to kill them. Despising one who openly commits sins and persists in his transgression is commendable if it stems from a rejection of his evil and zeal for the religion, as opposed to it being out of arrogance and self-admiration.