You're asking a lot of questions here, most of which aren't really specific to fight.
When a spell or ability resolves and says that two creatures fight, they each deal damage equal to their power to the other. That's all, nothing crazy.
When something depends on the power of a creature, like fight does, you always look at the actual net power of that creature. If you have a creature with base power/toughness 1/1 with a +1/+1 counter on it, and an aura that grants it +2/+2, it's a 4/4, so it deals 4 damage. If you have a plain 4/4 with nothing else going on, it's also a 4/4, and deals 4 damage.
Since fight only cares about the power of the creature, the toughness doesn't matter until after you're done resolving the spell or ability. If at that point a creature has been dealt damage greater than or equal to its toughness, it dies. It doesn't matter what dealt the damage - in this case it was fighting another creature, but it could just as easily have been a burn spell. It dies either way.
As for the bit about activating abilities and casting instants... that doesn't really make a whole lot of sense. You probably want to go have a look at how the stack works. There's only one spell or ability resolving at a time. If you cast Pit Fight to make two creatures fight, that goes on the stack, then players can respond with instants or activated abilities, which resolve first, and then when Pit Fight finally resolves, the creatures fight, plain and simple.
Remember, "fight" is an instruction you follow when resolving the spell or ability. It's not a little subgame with special rules and actions inside it, it's just a part of resolving a spell or ability that causes some damage to be dealt. When resolving a spell or ability, you can't cast spells or activate abilities, whether or not fight is involved.