Snero:
I don't know the contents of the rest of the site but googling "judge not lest ye be judged" gives a pretty good answer to why that quote isn't appropriate to any conversation
http://www.capalert.com/judgenot.htm -- Essentialy: the quote isn't don't judge or you will be judged, it's really Judge, but make sure that the way in which you judge can be used against you without you coming into fault over the same issue. By the same measure you are judging you will be judged.
Your quote about casting the first stone is a bit trickier however you'd have to know the whole context. The pharisees brought a woman caught in adultry to Jesus and asked what they should do with her. Notice there's no mention of what happened to the man caught in adultry nor was there a true desire for "justice" in the hearts of the pharisees. Jesus knew this and wasn't going to play their games. They were playing the ultimate hypocrite and Jesus called them on it. Another Link:
http://www.keyway.ca/htm2004/20040811.htm
Thou shalt not kill: Another good commentary on the subject:
http://www.apostolic.edu/biblestudy/files/6th-com.htm Basically stated: there are times when killing is necessary but murder is always murder. Thou shalt not kill is not referring to ending the life of someone, but instead of murdering them.