You do not lose any meals or snacks if you don't use one on a particular day. Your meals and snacks are there for you to use at your leisure for the length of your stay however you want to use them. No you cannot fill your mug up at the parks. It is for use at your resort only for the length of your stay for coffee, soda, etc. As far as dinner shows, I'm not entirely sure if all accept the dining plan or only some of them. Somebody else will definitely be able to answer that for you.
This will be our forth year in a row using the dining plan. We love it because we don't have to worry about paying out of pocket and what everything is going to cost on a day to day basis. It's already taken care of and very convenient. Others will tell you they hate the dining plan. Happy planning!