Soo.. do the eggs that are found in each planet spawn randomly all the time... or is there something you can buy to generate more rare eggs?? Like is there a specific time look for more rare eggs or is it ALL just by luck? I’ve been getting the same eggs. 

Egg hunting is currently just based on luck! You are likely to keep finding the more common species but if you keep hunting you might be lucky enough to find some rarer ones. You can check the rarities under the species directory (Information tab, Creatu Species page). Some species have a 0% rarity which means they can't be found by exploring.

Makes sense! Thanks so much :)