You can override any system setting in you ~/.kde directory. :-)
If your icon theme is, for example, Crystal SVG then kmenu will be using the icons under /usr/share/icons/crystal-svg/<size>/apps/kmenu.png.
If you reproduce the same structure under ~/.kde/share/icons/crystal-svg/<size>/apps/ directory but with diferent icons then kmenu will use that icons.
About the text in desktop icons. As far as I know you can't do that.