Short answer is,
Metal enclosures are required to be 'bonded'.
NOT to the neutral conductor, except in MOCP equipment.
The other questions can be answered by you reading a book on basic electricity.
You may want to consult a Qualified Electrical Contractor regarding the space heater as you may be endangering yourself or your property by attempting to DIY.
I am closing this thread as the forum rules do not allow DIY.