No, the eukaryotic cell does not have chromosomes in the cytoplasm but it is enclosed within the nucleus.
Yes by: Anonymous
Of course they do.
No by: TropMonifique
No I don't think so. The nucleus protects the genetic material, I think if it were spread to the cytoplasm the protection would cease to occur and mutations would be more frequent. It's not like in prokaryotic cells where the genetic material floats in the nucleoid area.