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?
Basically, Edward has always been for what makes Bella happy, no matter the consequence. In a sense, his allegence to her is higher than that to his family. While with Jake, he wants Bella to be just as happy, but not over what he feels compelled to do, which is fight with his brothers. No matter if Edward was or was not in the picture, I think Jake would have fought that battle whether Bella wanted to or not.
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 just don't think he feels competent enough to take on that responsibility. Haha yes, I think one day he will step up to that position...
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?
Alice loves having things her way. She loves designing and now that she's certain Bella will always be part of her family, she wants her "initiation" into the Cullen family to be perfect and she wants to be the one responsible for it. It's pretty much an act of selfishness, but she does want Bella to be happy with it at all costs.
WARNING: EDWARD CULLEN IS NOT EFFECTIVE BIRTH CONTROL! E<3B