I am a self-employed academic tutor and writer. This past year, I did work for a Chinese company that connected me with Chinese students. I was in the US, they were in China, and we worked by email. The company paid me just through wire-transfers (no other official documents). Do I have to report this income separately as foreign income, or do I lump it together with the rest of the money I made through my tutoring business?

You as a self employer and US citizen are subject to taxes to IRS/your state on your US source and world wide income transfered to you from china is your I guess world wide income so you must lump it together and claim taxes paid to china on your US return by filing f 1116 for claiming foreign tax credit.you may claim the taxes paid to china on sch A of 1040 or on f1040 line 48.you still need to pay quarterly estimated taxes on your income that you earned from China as a self employer