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?
I think that the difference between Jake and Edward is that Edward exists for
Bella, and Jacob is trying to exist with
Bella. Edward is staying because he thinks that Bella will react badly if he doesn't, which is true, but she has selfish motivations. Jake, on the other hand, Is trying to prove to Bella that nothing bad is going to happen, and that he's able to take care of himself. They're both trying to take care of her, but in different ways. Even if Edward wasn't in the picture, I think Jacob's answer would still be the same, just because he's trying to correct the way Bella perceives things, whereas Edward just accepts them as the truth from Bella's point of view. 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?
Absolutely. I think that Jacob is sort of... how do I say it...? Quietly rejecting being a werewolf, I guess. Like how he tried to explain to Bella that he was more human than Edward, I think he's trying to stay connected to Bella in remaining as human as possible. 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?
I think that Alice is so intense about the wedding not only because she likes to do events, (although that is a part of it) but because this is her way of showing how much both Edward and Bella mean to her. She's been Edward's sister for years, and she must have seen Bella in his future in some
way, so even before they became friends, Alice would have already loved Bella like her sister. So I think that she's just giving them the most elaborate wedding present / "I Love You" gift ever.