I flew last month from LAX to Shanghai direct, then Shanghai to Chennia, India through SriLanka, then Chennai to JoBurg through AbuDhabi and then from Joburg to Bulawayo and back to Joburg and finally from JoBurg home (through AbuDhabi).
I had two TSA approved combination locks on my case, which can hold I think six locks. No issues with that. Etihad told me I could not check a bow on their plane on my way home, but had no problem taking it over and I even showed them on their web site that I could check it, but the person at the counter called the manager and their manager would not budge. Even when I told them I flew over on Etihad with my bow, they told me that I was wrong and I did not fly there with my bow.
A bow is NOT a firearm. You have no restrictions that would apply to firearms with a bow. I packed lots of things with my bow, although not much in the way of clothes. I always keep the broadheads in my other bag and field points on my arrows in my bow case when I fly.