You're right. Adding "aru" at the end of your phrases sounds like Chinese, at least by Japanese people. That said, translating Meiling's speech into English is almost impossible because "aru" means "to possess something" while "nai" means "to not possess something.
You didn't include the "aru" part. My point is how can you translate the joke into English without changing the context. After reading the updated translation, I think it's turned out to be a good translation by adding the words "yes" and "no" in the same phrase.
Is Yuuka speaking to Meiling in Kansai dialect in the last panel?
By the context i assume she is just aggressive since Meiling was not clear, but if she is responding to Meiling's chinese dialect as bolger0 said it might be
This is probably a parody of a nameless antagonist in the mangaHokuto no Ken vol.20. He died an unreasonable death. His fans call him "ないアル (Nai-Aru)" or Aru-san.
Oh, yes! I have......ChinaHey, China!You got any meat buns?Oh, how convenient.Eh!? S-sorry.I'm getting hungry.It'd sure be nice if that China who looks like she carries meat buns were around but it doesn't seem like she is....no meat buns!Huh? Is it yes or no? Be clear, dammit.