Hi, welcome back!

If you haven't already figured it out, there are currently two main ways to find eggs:

1: If you hover over the "Explore" tab you'll get a dropdown list of the planets. Click on any of these except for Uldavi, and you'll be able to click around the planet and you might stumble across some eggs. 

2: If you click on the "Explore" tab, you'll be taken to our new pet exploration page. If you have an adult pet from your home planet, you can send the pet out to explore, but it can only explore the planet that you are a resident of. You can adjust the settings so that it has a preference for collecting eggs. 

Your old pets are probably in your tle="" target="_blank">graveyard and you'll be able to revive them with resurrection potions. I suggest setting up a showroom (click on the white dog in the upper left corner) - you can store your pets in there and they won't be at risk of dying as you don't need to feed them, although they also won't age. 

Let me know if you have any further questions!