I would suggest some silicon grommets. Buy a few and just layer them until you get a good seal. The stem should then sit flush with the base hopefully eliminating the wobble.
Those are the grommets I am talking about.
For the "coolness", could be many things, mainly your setup as far as packing and heat management. If this is your first personal rig you'll probably have to experiment with different tobaccos and coals. Every tobacco has it's own characteristics and heat tolerance. It can be frustrating but it's mainly trial and error. You'll find what works for you. I'd look through some of the videos and see if you can find any tips. Just keep with it.