I got a cartilage piercing mid june. Can I take it out to sleep?

The cartilage piercing takes a long time to fully heal. One of the advantages of a cartilage piercing is that unlike lobes most people do not change them daily. The advantage is you find a comfortable earring and just leave it in always.

Nope - it needs to stay in until it's fully healed (which takes at least 6 months)

You could but those piercings don't often fully heal for 6 months or more. They're one of the hardest piercings to fully heal

No.
This piercing takes 6 - 12 months to fully heal, 12 months minimum if done with a gun.
If you remove the jewelry of a healing piercing, it will immediately begin to close.
Your piercing is still healing.
If you take it out, leave it out. If you want to keep the piercing, keep the jewelry in.