Does your light go brighter than normal when it dims or just back to normal brightness? If it goes very bright, check from neutral to ground and see if there is any voltage present. If there is you have a loose neutral on your electrical panel. I've ran into that several times over the years...
It's a screw starter, you put the tip in the slot of the screw and slide the sleeve forward to expand the bit into the screw slot to hold it. They are very handy when you are installing short screws overhead or on a vertical surface. They are only for starting the screw, not torque.
Keep that soldering gun, the new Weller guns use set screws to hold the tip instead of nuts like yours, the new style guns often lose connection to the tip because of the set screws and stop working.
Get a Dynaplug kit at Harbor Freight, I've fixed two flats with mine and they are still going strong. I just wish they sold them somewhere besides Harbor Freight.
The new style weller guns use set screws instead of the nuts like the older ones, and they just don't seem to stay tight. I think the new ones are only good for replacement housings for the older style guns.