Theres a few different things to breed for, the main are rarity, boosts, defects (usually coat defects), and good vitals
the best ways to make mushrooms are to explore (killing all enemies and prey), sell wolves, put males up for breeding, and selling art. There's more, but these are really the basics
for the stats, you should focus on battle, resolve, and agility. they help with battling and killing prey/enemies. Stealth helps track prey, and the rest (other than maternal, charisma, and dominance) help complete encounters
yes, the wolves with the most dominace are your alpha male and female. Add CP to a wolf's dominace to increase it. the 2nd highest dominace will be your betas, the rest are omega/juveniles and pups. To decrease dominance, you can buy a stare down from the barter or use a road runner feather
Spring Month: 2 
Night 
Heavy Rain Moon: 
