How hard would it be to find a position in China if I don't speak Chinese? Are there certain places I should look for information on this? Job websites?
Best option is to actively solicit contacts and network a lot. Foreign professionals are a closely knit club here. Industry events are the best if you know nobody here.
Look for job offers in English, job boards of companies with a record hiring foreigners, foreign companies that are new in China, super senior level positions, jobs with PhD. level expertise level, jobs requiring people skills in English "product managers/ field application engineers/ sales or solution engineers"
Websites: 51job, zhaopin, ChinaHR. Look for English language keywords. A post in English almost certainly assumes the company keeps hiring a foreigner an option.