1. It's to the right of start. Once you go in the food market just hug/grab the wall on the top by goons npc.
2. Not really sure what your idea of "rares" is, im guessing auctioned items? You could trade with people ,etc. But I don't suggest this, as you will probably end up getting scammed.
3.Hm, good question. I spent my spare eggs on hats. There are some pretty decent hats in the shop.