hi
we were a bit 'slow' with transferring Maja to the bathtub [we bathed her in our living room, on the coffee table
until she was 7mo or sth, lol].
anyway, never have used the bath seat, only the tub pad. works great for us.
the amount of water- up to her waist line more or less.
washing her hair- well, you still can lean her backwards to wash her hair and avoid the water going to her eyes, but TBH I don't do that at all now, dd's used to having the water on her face and even in her eyes and is fine with it.
toys- those rubber ducks really ARE a great thing!