You may apply for a re-entry permit (I-327) by filing form I-131. The re-entry permit has the similar function as a passport (or the travel document) when you return to US. With your GC and I-327 you can come back. I-327 also looks like a passport with visa pages.
It won't hurt you if you apply for a ordinary passport in China.
It won't hurt you if you apply for a ordinary passport in China.