The threads are on the section, will unscrewing the cap unscrew the section as well?
The section will not loosen from the body when you unscrew the cap. The threads between the section and the body are left-handed threads, which are opposite of that of the threads between the cap and the section. Moreover, there is an o-ring between the section and the body, which creates more friction.
Do I need to add silicone grease on the threads?
It is not necessary to add silicone grease on the threads. The threads that will come in contact with the ink have o-rings that prevent any leakage. However, if you wish to be extra safe, it is okay to do so.