Yes, It is safe to watch the royal Bengal tiger from the Sajnekhali watchtower because this tower is covered by a ferrous weir which can give full protection from the tiger.
Yes, It is fully safe to visit Sudhanyakhali watchtower because armed force gives security to all tourists.
Yes, Permission is required to enter Sajnekhali watch tower. Most probably all travels agents get permission from the relevant department for their tourist.