I was wondering.. is the air quality in Gansu really that bad?

Well, the air quality is really bad in there. If your throat is sensitive, it is really not a good place to go. Surely people in there would have their dialect, it may be hard for you to understand also.
For your situation, you're suggested to go to Chengde (in Hebei) Hanzhong (in Shaanxi). These cities are not developed so prosperous as Beijing, Shanghai and others, but you will have fresh air there. Also you will find a Chinese language course easily. During work time, most of people would use Putonghua. Even if they not, it would be easier for you to understand than the dialect in Xiamen.

Well, I survived Harbin, so my thoat isn't THAT sensitive, haha. Thank you for your advice, but I really wanted to live in some not-so-obvious part of China, close to Xinjiang and/or Tibet, so I was thinking about Qinghai, GS or Yunnan/Sichuan. Also I love muslim cusine, so on this side GS/Qinghai would surely be nice!

I'd second that! I went to Chengde a few years ago, and I was astonished by how clean it was. It's probably the cleanest city I've ever been in in China. Plus, if you're interested in ethnic minorities, there are a good number of Hui people there, and you're not too far from Mongolians.