My hen is missing feathers around the base of her tail. We do NOT have a rooster so it’s not from mating. I noticed she had a watery poop today; not sure if it’s related. Any ideas?
There are other cause of feather loss on the back like that besides rooster mating. If your hen is old enough for molt, it can begin along about this time of year. Other chickens higher in the pecking order can be pecking this hen on the back to keep her in line. Sometimes feather picking and eating can indicate a dietary issue. Then there is the possibility of a near miss hawk attack that resulted in feather loss but not loss of life.
My money is on other chickens picking at her back feathers. Set yourself up to observe your flock some afternoon when you have time. You may be able to see the action and identify the feather plucking culprit. Then you may be able to take steps to stop the behavior.
If it's molt, it's easy enough to verify. If you see uniform pin feathers emerging in areas of feather loss, it's molt. If there are only broken feathers and bare skin, it's feather picking.
I had this happen when my girls didn't have enough space. It fits into the feather picking that @azygous mentioned. It's a difficult thing to break once it gets bare back there as the emerging pins seems so tempting to pluck for the others.
I've found that Blue-kote painted onto the bare skin and pin feathers can disguise them, thus discouraging pecking at the tender pin feathers. They are call "blood feathers" because they are rich in blood, and chickens can develop an addiction to them. Getting out in front of this behavior is important. Get some Blur-kote and be ready. I apply it with a Q-tip so it's easier to get it where you want it without making a bloody big mess.