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?
No, I truly don't believe so. Even if Sam didn't order him to fight, I believe that Jacob would still fight, if he was sure Bella wouldn't be harmed physically while he was gone. He would just tell her he'd be back soon, and take off. Then when he came back, he'd tell her that he was right, and she shouldn't have worried for no reason.
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?
No, I think he doesn't want to be a part of the werewolf thing, and has only done so reluctantly. Becoming the leader is just making it more official and more responsible.
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?
No, she's being selfish. It's probably back to the vicarious part of her nature - living out her humanity through Bella.