Do people with the covid coronavirus get any diarrhea? if yes, how bad is the diarrhea, and what portion of infected people start having diarrhea?

No: To date the process has been a respiratory virus. No gut issues (diarrhea,etc.) are reported so far as part of the symptom pattern.

Respiratory illness: Cough, fever and shortness of breath are most common sx's. Per Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus–Infected Pneumonia in Wuhan, China - JAMA, Wang et al., February 7, 2020 - about 10% of hospitalized patient had diarrhea. This study only looked at people who were so sick that they had to be hospitalized. This is a small study number.

Yes, diarrhea is now considered one of the common symptoms of COVID-19. Although respiratory symptoms are still the most common, headache and diarrhea are now fairly common. Approximately 20% of patients with COVID-19 have diarrhea as one of their symptoms. https://www.cdc.gov/coronavirus/2019-ncov/symptoms-testing/symptoms.html