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.
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Assuming the defending monster is also in attack position, both monsters will be destroyed.
Your monster is destroyed if the monster you attack is in attack position, and you lose life points.
When a monster attacks a defense position monster with DEF equal to to the attacking monster's ATK, no damage is inflicted to either player's Life Points and no monsters are destroyed in battle. Some monsters have effects that activate before or after they battle, so you must take those into account as well.
No. When a monster you control attacks a monster with a Defense higher then the Attack of your monster, you take damage equal to the difference but neither monster is destroyed. The only exception is due to card effects such as Des Kangaroo.
Answer taken from the Official English Rulebook: After you've announced your attacking monster and the attack target monster during a Battle Step, the attack target might be removed from the field, or a new monster may be played onto the opponent's side of the field before the Damage Step, due to a card's effect. This causes a "Replay." When this occurs, you can choose to attack with the same monster again, or choose to attack with a different monster, or choose not to attack at all. Note that if you attack with a different monster, the first monster is still considered to have declared an attack, and it cannot attack again this turn.