Both sentences are mostly correct. I will explain them in a simple way and show a few better options.
Original 1: During the day, red pandas nap up in trees, and at night, they wake up to eat.
Notes: This is okay. You can say "up in trees," but usually we say just "in trees." The comma before "and" is fine because it joins two full parts (clauses). A simpler version is:
During the day, red pandas nap in trees. At night they wake up to eat.
Original 2: Red pandas nap during the day and are out to eat at night.
Notes: This is understandable, but "are out to eat" sounds a bit odd. Better choices are "come out to eat" or "wake up to eat." For example:
Red pandas nap during the day and come out to eat at night.
Best short sentence you can use:
Red pandas nap in trees during the day and wake up at night to eat.
Good job noticing these sentences! If you want, I can make them even shorter or turn them into a tiny story about a red panda.