1. Is it mandatory to have a valid AP to temporarily leave US while 485 is pending?
-Not really. You can use H (H1 or H4) or L (L1 or L2) visa to come back without affecting I-485 if you current status is H or L.
2. If I arrange my trip return date before 12/20, I should be fine right?
-Yes.
3. Is there any issue if I renew my AP after it is expired?
-No problem at all.
4. In my AP page, it says valid "prior to 12/20". Do it mean before and include 12/20?
-Not include 12/20.