1. No the plug does not move.
2. The part you are trying to remove is the emulsion tube. The end of it sticks up into the carb throat. Take a screwdriver and stick it in past the choke valve, and use it to push on the end of the emulsion tube. Once you've pushed it down as far as you can, do some more banging on the work bench and it should fall out. If it doesn't, take a right angle pick and push it down some more.