Is killing forbidden in Islam?

Here is what the Quran actually says at Sura 5:32:

On that account: We ordained for the Children of Israel that if any one slew a person - unless it be for murder or for spreading mischief in the land - it would be as if he slew the whole people: and if any one saved a life, it would be as if he saved the life of the whole people. Then although there came to them Our apostles with clear signs, yet, even after that, many of them continued to commit excesses in the land.”

This injunction applies only to the “Children of Israel,” which is to say, the Jews. This is not meant for nor does it apply to Muslims.

This verse allows Jews to kill someone if that person is a murderer or if that person has spread mischief in the land, such as adultery, fornication, waylaying, etc. 

And how should those who spread mischief be punished? What Muslims will not quote to infidels is the very next verse, 5:33:

Indeed, the penalty for those who wage war against Allah and His Messenger and strive upon earth [to cause] corruption is none but that they be killed or crucified or that their hands and feet be cut off from opposite sides or that they be exiled from the land. That is for them a disgrace in this world; and for them in the Hereafter is a great punishment,