only with a cards effect. during a normal battle, you can't just simply set it.
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Yes. Once per turn, a monster may switch from face-up attack mode to face-up defence mode, or vice-versa, as long as the monster was not summoned that turn, and had not declared an attack. If the monster is face-down, then turning it face up into attack mode is a Flip Summon, which can't be done on the turn the monster was Set from hand.
A monster flipped face-up by a card effect, such as "Book of Taiyou" or "Stop Defense", or as a result of battle is notconsidered a Flip Summon. Only flipping a Set monster manually is considered a Flip Summon.So if you attack a face-down Stealth Bird, it will be flipped but not Flip Summoned, so its effect will not activate.
Nothing, unless the card specifically mentions a penalty for not attacking. If a monster is in defense mode it is not able to declare an attack, and there are no consequences for not attacking unless the monster's text mentions one.
Destroying a monster does not flip it. But if a monster is flipped face-up when attacked, and considered destroyed by battle, then the flip effect will still activate.
You can manually change the battle position of a monster once per turn, (but not on the turn it was set or summoned from hand) If you flip a monster face down with Book of Moon or use the effect of Sonic Bird, then you are allowed to flip summon them in the same turn.