1. No - there is no requirement for a further medical. (See the list of required documents on page 9 of the application form.
http://www.immigration.govt.nz/NR/rd.../0/INZ1020.pdf) Variation of conditions is just a continuation of your present visa.
2. As far as INZ is concerned, as long as you make it clear to them that that is what you want and intend to do, because your visa must clearly show what your work situation currently is, yes. Obviously, if you or your present employer had given notice, bringing your employment to an end without moving to another would bring your present visa to an end.
http://www.dol.govt.nz/immigration/k...base/item/1187