you can bring food as long as its not a liquid, gel, or cream.
for example: jar of peanut butter= NO, peanut butter sandwich= YES. (lame, i know.)
yogurt= NO, banana= YES. tub of frosting= NO, frosted cinnamon roll= YES.
also you are correct, no drinks allowed thru security; but you can buy something at a gift shop or restaurant once you pass security and bring it on the plane with you.
any liquids, gels or creams whether food or not, you are allowed ONE QUART-sized zip-loc style baggie filled with 3.4oz containers only. not 2 baggies, not 3.4oz containers with no baggie.
specific guidelines can be found at
TSA | Transportation Security Administration | 3-1-1 on Air Travel
ps im not a know it all, i work for an airline