If I restart Pokemon Moon, will I lose all my Pokedex Entries in Pokemon bank? I have like 792 out of 800 Pokemon Seen and Caught in the Pokedex in Pokemon Bank, but if I restart Pokemon Moon, will those entries disappear?
The entries in your bank won't dissapear. Your Pokemon Games and the Bank are 2 different things. What's in the bank will stay there unless it's reset/deleted from the bank. I think that for now the only way to do this would be to not renew your subcription for 6 months after it ends so Nintendo will delete every data about your bank. (Don't ever let this happen if you have pokemons in there).
For your in-game pokedex if you want your entries back you'll have to move manually all the pokemons you have in your bank back in your game at least once.