Do I need to hatch my Egglings in about a certain amount of time or can I keep them in my Hatchery as long as needed? My stable is almost full and I have too many Egglings, which is why I can't hatch all of them.

Its ok eggy hatch on their own, if you are there at the right time, your eggy will prompt you to make a choice, help it out of the egg, let it hatch by its self, or give it a philter. Then your eggy becomes a hatchling wich still lives in your nursery. Eventualy the hatchling will grow into an adolescent, there you can either let it live in your nursery or move it to your stables. After a few days your adolecent ages into an adult, this time it will automaticaly enter your stables, if you lack room the pet is released into the wild.

Okay. Thanks. Also I didn't know Egglings can hatch on their own. That's cool.

Yep if you are not around when the eggy desides to hatch, or you miss the time, the eggy will hatch on its own. Do note that eggs that hatch without your help on the propt will not have the small bonus they reseve when you do help.

(Yes pets will hatch on their own after a certain period of time- I'm not actually sure how long, might be 24 hours from the point when they hit 72 hours? Something like that)

They remain in the hatchery until either they're moved, or they reach adulthood at 648 hours/27 days old, at which point they will either transfer to the first open slot in your stables or be released if there is no free spot in any stable.