Re: you can shake a carrot stick at
The idiom is "more than you can shake a stick at." I don't know where it came from, but it means "many."
Because this is about dieting, and people eat carrot sticks as snacks (better than a candy bar if you're trying to lose weight), the author has made a little pun or clever use of language, changing "more than you can shake a stick at" to "more than you can shake a carrot stick at."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.