Nothing carries over to a new game, however you can modify the Medals.txt file to change the requirements, and even which class-specific medal a character can earn.
To change the requirements, open medals.txt and look for something like the following:
max1=10
max2=30
max3=50
Just change the numbers, and you've changed the requirements. Be sure to change the numbers for all three levels of the medal you're changing.
To change class, look for the following:
medclass=-1
Then update to match the class you want.
I *think* the values are as follows:
-1 = all classes
0 = Warrior
1 = Paladin
2 = Mage
Concerning tth pet, even though it can't be used in boss battles, it's very, very useful. I don't recommend getting more than one level of the skill which boosts the pet's experience (and then only to get to the skill immediately below it), but YMMV.
Pet experience increases if the opponenet army is greater in total leadership than your army, and it's dynamic - as you kill enemy units, their total leadership declines, so you get less xp for your dragon at that point. Typically, you'll get more xp earlier in the battle, so plan accordingly. Simply fighting many fights with a smaller army than your max leadership allows will make a big difference (just be sure to bring enough troops to win the battle
)
BTW, I know some folks really like Dragon Dive, but in the mid to late game, Ball Lightning will be really useful. And I like Fiery Phantom for area damage.
For mods, check the Mods threads. There are a number of them available, some of which are interesting (all troops on Debir, for instance).
For strategies, search the forums. Pretty much anything you're running into has been seen and discussed before, including goblin shamans and optimal strategies for impossible games.
Good luck!