Your second point is true. Actually, any object submerged in water (without any other contact) will have have a force equal to the mass of water that it displaces acted on it in the upwards direction.
From this point, if the object that is 4/5th submerged in water, it will have a force equal to 4/5 of its volume worth of water pushing it up. Assuming equilibrium, then, mass of object = 4/5 its volume worth of water. Water of the same mass will have 4/5 its volume.
Let Rhoo be density of object
Let Rhow be density of water
Let V be volume of the object
Rhow=m/v
m=v*rhow
Mass of object=Mass of water is displaces
v*rhoo=(4/5 v) * rhow
rhoo=4/5rhow
Therefore first point derived from second point. Hope this helps!
