Hiya.
I used to use QuArK for my level editing. All you have to do is save as .map. If you want to put the textures on in QuArK, you have to build yourself a .wad for QuArK using the textures you want to use; these should have the same name as your WED .wad texture pack. For example, if you want to use a texture called "stone03.bmp", you have to have a texture called "stone03" in both QuArK and in WED. Then, when you open your .map file you created in QuArK, as soon as you load the .wad that has "stone03" in it, it will show up on the appropriate blocks.
WED will also recognize lights, but not the light info; just the light itself, so you have to go light-by-light and reset their intensity, R/G/B, etc.
On the plus side, if you know what you are doing (programming wise) you could make your own add-on for QuArK so that when you save as .map it saves whatever you needed (lights with radius, intensity, colors, player starts, etc), but that would require you creating your own "pak" file for QuArK (like the 'pak' files for using Quake I, Hexen II, DOOM3, etc.).
I mainly used QuArK for it's ability to quickly build 'pre-fab' things and use it's "auto-builders" (like spiral stairs, stairs, etc.).