1. Already explained.
2. Thermal paste is used to fill in the gaps between the CPU IHS/core and the base of the HS. Because these surfaces may not be completely flat, the bare contact between a core/IHS with the HS base will cause increased core temps because the "rough" surfaces will trap in air. Since air is a poor insulator, heat will not travel very quickly from the core/IHS to the HS, and thus overheating may result.
3. Yes it helps
4. Thermal paste is almost a necessity; however, you do not have to use it. You will, however, probably decrease the lifespan of that specific component. Unless you can lap the surfaces that will come in contact with each other to near perfection, I highly recommend using thermal paste.