Sunnie, the short answer to you question is "no" - you can't eat unlimited quantities of meat and cheese. But you can eat generous, reasonable portions! If you look at the suggested daily menus for Phase 1, it will give you an idea of how many serving of meat, cheese, etc., per day. I don't have the book with me, but it seems like it includes 3-4 servings of lean meat (breakfast, lunch, dinner, sometimes a snack?) The serving at dinner seems to be bigger than the others. I think most days of the menu have about 3 servings of cheese. One ounce is considered a serving, I'm pretty sure.
As for non-veggie snacks, try lean ham or turkey slices spread with Laughing Cow cheese and rolled up, hard boiled egg, cheese sticks, a bit of tuna or chicken salad wrapped up in a lettuce leaf...there are really lots of options.
I'm sure the great folks here will be able to help you out!
It is easier to suppress the first desire than to satisfy all that follow. -unknown