Student visa then Family visit type now American tourist type no longer married How long can I stay?

American previously student in China, married to Chinese having one child (born in PRC), wants to make a longer than 30 day visit to PRC and spend time visiting family of ex-wife, ex-wife's family plans to provide a letter of invitation. Can I stay more than 30 days on a Tourist type? How long can I stay total on this type? How long can I stay if multi-entry tourist type? Thank you.

One more question, I hate to bother you. If someone wants to hire me as a teacher, and I am already here, can the proper authority change my Tourist type to Work type? If not, what is the most economical way for me to get it changed? HK or Macau?