Bella says this because Alice can see the future, so anything Alice predicts will most likely come true. Alice has seen in her visions that Bella will become a vampire. Edward doesn't want such a future for Bella. He's against it. And then Bella says - I'm betting on Alice. As in, 'I think she will be right'.
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Because Phill broke his leg in a baseball accident and needed someone to take care of him. In the book, it says that Alice invited them to her graduation party as a surprise for Bella.
In Breaking dawn before the wedding Just around the time when Alice begs Bella to let her plan the wedding and says he already has a rock on her.
She means that she isn't going to take a side.
In order for Twilight * Page 274 (Edward says it) * Page 314 (Bella says it) * Page 366 (Edward says it in many words) * Page 418 (Edward and Bella) * Page 456 (Edward says it) * Page 479 (Edward and Bella) * Page 498 (Bella says it)
He means that it is against nature and disgusting from a point of veiw but he love the lamb/Bella, I hope this answers your question.