1. Am I solely responsible to see that all the people in my department work safely and are in compliance with regulations?

No. DSRs certainly have a key role in coordinating and encouraging safety and regulatory compliance, but the real responsibility lies with individual supervisors/faculty and department administrators (e.g., Chairs, MSOs).   See campus policy #5400:

http://www.policy.ucsb.edu/files/docs/policies/ehs.pdf

Tag: 

IIPP - Department Safety Representatives