For the first question, all chins will put their ears down sometimes, especially during the day when they are sleepy. I wouldn't worry about it if that is the only symptom.
As for the barking, my male does it, too. We have had him for 9 years now, and it seems to happen when he is sleeping. Like he is having a bad dream and barking (alarm calling) at a situation in the dream. Once he wakes up, he is fine. Your chin may be dreaming. Chinchillas also have very sensitive hearing, and can hear sounds we cannot hear. They also react differently to sounds that are normal to us. For example, our chin was really stressed out for a long time every time we ran our new dryer. We finally realized it is because the sounds the dryer makes must be in the "predator growl" range, and his instincts told him to be afraid. He has gotten over that, but we still make sure the dryer is off if we want him to come out of his cage for playtime (he will NOT come out if it is on).
My advice is to spend some time with him and see when it is that his ears are down: is he asleep or sleepy, or is it even when he is awake? Also, find out what is going on around him when he barks: is he waking from a dream? Is there a low vibrating noise going on? Is there some other "threat" he is hearing that you don't?
Best of luck!