1) eggs should be ok for most people. You could be allergic to it without knowing it and if you are, this can set back your progress (I recently discovered I am mildly allergic to eggs and stopped them a few months ago and have felt quite a bit better).
2) I am unsure why the amount is higher but because of this, it should not be consumed on the diet until stage 3 as a cheat item.
3) Carrots are very high in the glycemic index and are high in sugar. When you juice them, this concentrates it and thus its really high in sugar. You need to limit your sugar intake as much as possible on the diet.
4) This is up to you. What pH level are you trying to achieve?