Yup, I would only rest for 30 seconds.  Since push-ups are specifically designed to give you more muscle endurance, you do not want your ATP and your muscles to fully recover between each set.  

If you eat right before you do them you'll have a lot of blood going to your digestive muscles, which will compete with the muscles used for pushups. On the one hand your muscles will have to work whilst being starved for oxygen, which will help to excert them even more, but on the other hand your muscles won't be first in line to get the nutrition ne4eded to build new muscle fibers.

The one thing to eat within an hour of working out is protein. Amount depends on how much you work out and how much you weigh.

There is no real mericle thing to eat to vastly improve your performance during your workouts. The best advice I can offer is to eat right all of the time and use your supplements wisely if you choose to go that route.

Supplementation is a whole nother topic, and one that I or several others here would gladly get into with you if you want.

You might find that periodic days off will help to keep from getting too flat in your workouts. They give your body a chance to recover fully and come at the next workout full bore.