Thumb shifters mount on the bars, usually out near the ends of the tops where your thumbs (duhhh) can easily reach them. They do not mount on the stem or quill.

Edit: I just saw your latest posting. 7-speed bar ends are no longer made but should be available NOS or used a lot of places.

You probably do have a freewheel hub so your choices are limited. There are 7-speed freewheels available but few gearing choices. The newer design is a freehub that takes replacable cassettes and offers a wider range of cog sizes.

If your spacing is 130 mm, that's not surprising as it was an interim MTB spacing when road bikes were still 126 mm and before MTB's went to 135 mm.

At this point, I recommend taking the bike to an LBS or Bike Co-Op and getting someone who recognizes exactly what you have to fill in the blanks.