Each Gym has different rules. For example, when you take over Noah's gym, only first-stage evolutions are allowed and only GROUND-types allowed. You have to use the same number of Pokémon Noah had on his team. This is to keep in line with the idea that the first Leader isn't supposed to be too hard for Amateurs. Then as you progress to take over Kate's Gym (Noah's is extremely quick to progress), you'll still have to use the same number of Pokémon she did, but second-stage evolutions are acceptable now, but you must only use NORMAL-types. Etc =)
And the Tournament isn't going to be 8 rounds long straight just like that with no healing inbetween, so don't worry! =P Depending on your previous choices and careers, your experience of the Championship Tournament will differ, as in the roster of opponnents will change. =)