Hi Debido!
Your appetite will definitely decrease on this diet, so I wouldn't worry too much about portion sizes. You should start feeling full after a meal within a few days.
Yes, you can have any of the allowed vegetables in between meals if you're hungry. It's good to have a couple of planned snacks throughout the day.
Check out the FAQ section here. There are a lot of good suggestions.
http://www.3fatchicks.com/forum/forumdisplay.php?f=115