For the specific questions made on this:
Attacks made with natural weapons (bites, claws, tails,...) are considered improved unarmed attacks, as they don't generate an oportunity attack, they do lethal damage and they are made without the use of a proper weapon. On many games and books these are emphasized just making that almost every creature that uses natural weapons has the improved unarmed strike feat. However, on a point in time I don't exactly remember, this became a fact in the rules. So yes, the stregthstrength modifiers for attack and damage are added to these attacks (although I've seen some games and books where certain bite attacks added only half strength modifier to damage).
No, that's not legit because, although actions can be executed in any order, they has to be declared before starting to execute any of them, so if you declare that your character is going to make a full round attack action and a bite attack free action, it doesn't matter the order in which you execute both actions, the fact that the bite attack free action is being executed affects the attacks for the full round action, even if the bite executes afterwards. You can attack your enemy with -2, kill him before even biting it, at had to bear with the penalty because you had the intention to bite him and you prepared your body, your stance and your attack pattern to it.