Not only is this possible, it's actually possible to do damage in the millions in (highly improbable) situations. For example, a level 100 Ho-Oh holding a Choice Band, with the ability Huge Power or Pure Power (not normally possible without the use of cheating devices) and its maximum attack stat/maxed out attack through attack stat increases can do 26,807,962 damage against a level 1 Paras with the Dry Skin ability and the lowest possible defense through its lowest possible defense stat/attacks that decrease defense.
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An HP UP increases the maximum number of HP (hitpoints) a Pokemon has. This allows it to absorb more damage from attacks before it faints.
Mega Kick does 40 more damage (120), but only has 5PP and 10 less accuracy points. Mega Punch has 80 damage, and 85 accuracy, and TWENTY PP. Clearly, Mega Punch is the better choice, unless you want a Pokemon with KO power instead of endurance in battles.
No, they do neutral damage.
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Fighting moves inflict 200% more damage on Normal, Ice, Rock, Dark, and Steel type Pokémon. A Pokémon that has a combination of any of these types will receive 400% more damage instead of 200%.