RE: Advice on Repair of Sig LT40
I think you can just glue the verticlal-stabilizer/rudder assembly right back on. Use epoxy. After it has cured, make sure it is reasonable attached and don;t kick it off again.
As far as the "fuselage cheeks", if I understand you right, these are just the pieces of the fuselage sides that extend in front of the firewall. These can be removed and thrown away as they are there only for cosmetics.
I can't really tell what is wrong with the steerable nose wheel. In your picture it looks pretty good.