1. Yours is probably a hybrid amp, meaning the tube is there as either a buffer or a preamp section in the input of the amp, which is then coupled to another amplifier which in turn will drive your headphones. The number of tubes used in a circuit varies in the design of the amp. A 12AU7 is a small signal tube in what is more commonly known as a "peanut" package, there are smaller/bigger tubes than the 12AU7 but this is mostly synonymous to power requirements of the circuit. A bigger tube will have bigger plates which can handle larger currents.
How does it affect the sound of the amp? Answers widely (and wildly) vary, some nut job would say that replacing the tubes shouldn't affect the sound, but later on, that same nut job would also say changing the tube would. You see, it all depends on your point of view and how your ears respond to whatever changes tube rolling presents to you. For example, to some, a Telefunken 12AU7 would differ in sound when compared to an RCA cleartop 12AU7, but there would also be some who would say it doesn't make a difference, maybe they just don't hear I don't know.
If there is one thing I learned in my years of tube use is that there is no fast rule. There maybe guidelines you can follow but these are highly debatable and usually starts a comical war.
2. You could ask the manufacturer of your amp, most China tubes are made by Shuguang but you know how China is, they can be making these in their backyards for all we know. Yes you can use other brand 12AU7, and other close or equivalent models like 5814, ECC82, etc...
Hope this helps. Cheers