I'm new to World of Warcraft (I bought my friends account and made some new characters and death knights) and I would like to know something about the sound addons that you can download, like DK Sounds or Achmed the death knight. if you are PvPing, in a arena or battleground or something of the like, can other players hear that sound? For instance, if I use strangulate on my death knight, with achmed the death kinght installed, I will hear Achmed saying, "Silence! I kill you!" But will other players hear me?

For the vast majority of them, other players won't hear it.  It's theoretically possible to make an addon that plays sounds for other people... but the other people would have to also have the addon.  There's no built-in way to make someone else's WoW play a sound without them having an addon that "listens" for a command to play a sound.