The round greenish eggs are probably going to be tomato hornworms, squish any you see, and you might want some BT spray. A tomato hornworn when it gets big can eat a whole plant in a day. When they are first hatched, they can be very hard to see--they are exactly the color of the tomato leaf. Try checking early in the morning when they tend to be out in the open. Later on, they tend to hide or be under the leaves. If the bites are very small, it's possibly damage caused by a caterpillar. If not, I'd still suspect some animal or bird. The only way I've ever found around that was to pick as soon as the fruit started to blush and let them ripen in a window. Here, the mockingbirds eat mine (and the squirrels, and probably the possums, too....).