How Do I Fix This?

Ok- my son, in a fit of pique, broke a floor standing lamp in our front room a week or two back, and it seems the piece(s) below are critical to it all working. However I cannot work out how to fix this.

The long threaded bar bit in the first picture is critical, and has snapped. It is threaded along its length. This comes up through the the lamp's floor counterweight (and is has a bolt attached to it to hold everything together on the floor side of the counterweight).

The second shows the bottom of the stem of the light. This has a thread on the inside (which you cannot see because the end of the long threaded bar is snapped off on the inside. Basically this double threaded piece screws onto the threaded bar to provide the upstanding stem of the light something to be secured to the base.

If that is as clear as mud, sorry. I have 2/3 questions though.

1. How do I get the broken bit of the bar out from the smaller double threaded bolt?

2. Assuming I can get the bar out, where can I get a replacement?

3. If I cannot get it out, any ideas where to go for a replacement for both parts.

Any thoughts most gratefully received as otherwise I need to buy a new lamp.