his mouth being open is a good sign, don't worry. It means he is thermo-regulating his body temperature by letting the extra heat dissipate through his mouth. In other words, he's warm enough. It can also be a symptom of respiratory infection, but this isn't the case 95% of the time- unless he's doing it even when he's not under any heating light.
The arm waving is a sign of submission. He's showing you that he means you no harm, that you're his superior. This is actually a very good sign, and you can bond with him by slowing waving back in the same manner: it'll show him the same thing, that you mean no harm and he can trust you.
Congrats on your new friend !!
