Not sure why this is downvoted since it's 100% correct. I always bring food through security, sometimes it gets flagged going through the xray machine but all that happens is TSA has to manually look through your bag. Normally as soon as they see it's food they just let you go, I think it's pretty common.
Yes. I think pretty much anyone that has flown with young children could backup that you can bring food through. We bring all sorts of snacks for the kids. Fresh fruit, crackers, cheese, etc.