Hi Acadia,
     As far as using the paint bucket tool to fill an area, try increasing your tolerance.  Depending on the size you might still have to click more than once.
    For pasting after you copy or cut the part of the image you want, go to file -> new.  A new file will be created to the size of your cut/copy and at the same resolution you cut/copied  from, after the new file is created just go to edit -> paste and there you go.

Hope this helps.

 

Stew