Veggies can and should be given to rats daily but on a very small scale and only 2-3 things per day on a rotating basis. I've always given my ratties veggies daily. If I give lettuce, it's a piece about the size of a coin half dollar. If it's cucumber, it's a piece about the size of my thumbnail, if it's carrot, it's a very thin matchstick size piece. 1 sprig of cilantro, etc.
1 cup is way too much.
Baby foods aren't the best thing to give rats. It's ok once in a while, but I've only given it sporadically, I've mainly used it for sick rats. Sunflower seeds are very fattening and should be an occasional treat.
You want to be careful of any sugary foods. Cereals need to be very low in sugar and the organic ones are best like the ones from Natures Path and Arrowhead Mills.
Hard boiled eggs are good but they also are pretty high in protein so once a week is fine for those.
I like cooking natural grains for my rats like amaranth, quinoa, brown rice, whole grain pastas, plus I give some of these uncooked too.