what are the maximum number of 90 day entries into china per year?

If you can get a China visa with 90 days stay duration per entry, you can stay for 90 days, then exit and reenter for another 90 days with another valid visa.

If you get a double/multiple entry visa with 90 days stay duration per entry, you can stay for 90 days, then exit and reenter for another 90 days. You don't need to apply for a new visa.