Nuclease are enzymes in a cell that break apart RNA and DNA so that their parts can be recycled, and yes human cells contain these enzymes.
If you meant nucleus, which is where the DNA resides in a (most) cells, then yes, most human cells contain a nucleus (the most notable exception being red blood cells).
Never. Only bacteria may have plasmids. Plasmids are circular pieces of DNA that carry genes for extra functions, usually beneficial to the bacteria like antibiotic resistance.