"Cap" is a slang term for kill, usually with a bullet. It comes from the ignition cap on the cartridge for a firearm. "Somebody capped him last night." "Pop/Bust a cap into somebody" - fire a bullet into them. "If I find the guy that broke into my house, I'll bust a cap into him." I'm not sure about some of your examples. In 3, it sounds like "hit" someone, but I'm not familiar with that slang. 1 may refer to psychedelic mushrooms - the piece being the stem and the cap being the top. [But now that I see Peachy's interpretation, his is probably the right interpretation for (1) - sorry]

What guy are they going to cap?

Here the word "cap" is a slang term related to guns and shooting 1- I have a piece[ gun] but no caps. [ bullets] 2- If you don't quieten down, I'll have to cap[ shoot] you. 3- Slow down or I'll cap [ shoot] you one. 4- They said they were going to cap [ shoot] that guy.

"Cap" in these examples mean "bullet". As an action - to cap someone - it means to shoot them. "I have a piece but no caps." means I have a gun ("to carry a piece" means to have a gun on your person) but no ammunition.

It depends on the context, try this dictionary link: http://www.thefreedictionary.com/cap