Please refer to this guide on how to purchase L99 from Pancakeswap.
Eggs in store
Depends on your Egg type that you will have different hatch time. Detailed about the eggs can be seen here:
You can view your Eggs in Stable section.
Choose your eggs, after the countdown ends, you can hatch the Eggs and receive Unicorns
Click on Hatch
You will need to pay Hatching fee.
Voila, you can participate in other activities of the game. See here to have a look of different types of Unicorn.