I was able to fix the exceptions by providing custom property 'name' in WAS DataSource equal to schema name. The schema name actually can be different. For example, WL 6.1 DDL scripts define it as WRKSCHM, but WL 6.1 Info Center as WORKLIGHT.
So, I preferred WORKLIGHT as schema name and re-run DDL scripts. After that I have added the 'name' custom property in Resources > JDBC > Data sources > Worklight Database > Custom properties as shown on the image.