You can "cycle" your tank by peeing in it yourself.
All you mean when you say "cycle" is to provide nutrients for bacteria in order to stimulate their growth in anticipation of fish someday doing the same.
1) Live rock does this naturally. If you have live rock in your tank, you need nothing else to provide food for the bacteria.
2) A dead shrimp works fine too. As it decomposes, it releases nutrients for the bacteria. Adding uneaten food to the tank does the same thing.
3) Any living fish would work, but it's mean to the fish... no mater what fish you use. And it's likely to kill it. If it doesn't, it'll surely **** it off.