If you look at the menus at allears, it tells you what is included. Most adult food does not come with drinks. But most kids meals do.
Your 13 year old will be charged as an adult for buffets (some have drinks included, not specialty drinks both OOP and DDP).
Your child does NOT only have to eat off the adult menu. Anyone can order kids meals at CS places (I often eat them, especially for breakfast) and pay the kids prices. Anyone can also order anything off the kids menu at TS restaurants (though sometimes they may have to pay more, but get more food).
GENERALLY, unless you are big eaters and have several TS meals scheduled (especially those worth 2 credits) the dining plan is not financially worth it. HOWEVER, if you are the kind of person that will nickel and dime yourself when it comes to eating (and not eat what you want because it's too expensive), then IMO it becomes worth it.
(More than you asked, but I know you've asked about the dining plan several times).