If the attacker has a higher ATK than the defender's DEF, then the defender is destroyed. No damage is dealt to the defending player's lifepoints unless the attacker has a special effect that allows it to do so.
If the attacker has the same ATK as the defender's DEF, then nothing happens. Neither monster is destroyed, and neither player takes any damage.
If the attacker has a lower ATK than the defender's DEF, then the attacking player takes damage to his life points equal to the difference. The attacking monster is not destroyed though.
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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.
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.