If a face-down monster is attacked, it is flipped face-up and maintains its battle position. Monsters can also be flipped by the effects of other cards. Neither of these methods are considered to be a Flip Summon.
There is no rule that allows players to flip face-up monsters face-down. This can only be done by the effects of certain cards.
Some monsters, known as, effect activate when they are flipped face-up.