With the right traits, non-active Sims could easily be rude to your Sim. Mean Spirited and Inappropriate would be a good combination to get a Sim to do that on his/her own, regardless of relationship. There are probably a few others that people could come up with that would help facilitate this, too. That's just off the top of my head.
As far as killing other Sims, there are no social options that will lead to the death of another Sim (I assume that's what you're looking for). You, yourself, have to create situations that will cause Sims to die. Some options are to build walls around them with no doors so they starve, position electronic devices in puddles and have the victim work on it (requires control of that Sim), create a swimming pool and then build walls around the edge so they can't get out, or create a "burn room."
The latter is by far the most complex, usually. You need to create a room that contains an object that will catch or cause a fire (like a cheap stove or cheap fireplace), and then cover the whole floor with rugs. When the object starts a fire, the rugs will burn as well and the victim will have no place to go.
If you're using the stove, you have your Sim call the other Sim into the burn room with you and then move the door so they can't get out. You then start cooking, but cancel the action once it reaches the stove phase. Finally, you cancel the action, replace the door, have your Sim leave and move the door again. A fire will ensue shortly.
The fireplace method is a little more tricky and less efficient. If you're killing Sims that are not under your control, you have to upgrade the fireplace with the "Auto-Light" upgrade. You build the room with the fireplace and rugs, call the non-active Sim into the room, have your Sim leave and then remove the door. Since the lit fireplace is the only object in the room to interact with, the Sim will poke the fire compulsively. Eventually, the poking will ignite the rugs and the Sim will essentially kill themselves. It's theoretically possible that the Sim could starve to death before they burn to death.
It is also possible that the Sim in question might survive the fire.
