1- What is it about Edward and Jake that makes their answer to Bella’s request that they stay behind and not fight different? Would Jake’s answer be different if Edward were not in the picture?
Jacob and Edward are simply different people. Even if Edward wasn't in the picture, Jacob still would have wanted to fight.
2- Is there something more to why Jake doesn’t step into the role of Alpha Male? Will he decide to become chief later on?
I honestly don't know.
3- Why is the wedding so important to Alice? Is her motivation truly for Bella’s (eventual) happiness or is she being selfish in wanting to coordinate a big event?
She's just being selfish, haha. She can't resist parties.