Quark saves linked images with absolute file paths; unlike web-oriented programs or Acrobat which use relative paths. The only way around this I know is to keep the document in the same folder as the pictures; then it "knows" where to find them if the containing folder is moved.
The "correct" way to import pictures into Quark is to select a picture box (any drawn with the tool with the X in it) and choose "get picture" from the file menu. This is different from Pagemaker, where you click a tool to place a picture, or the MS applications where you usually select Insert Picture at an insertion point.