These are some good starting places for chemical safety information. More databases, websites and handbooks are listed on the Chemical Safety Information guide.
Along with the Department of Chemistry and Biochemistry's Lab Student Safety Education page, please consult UC San Diego's Department of Environmental Health and Safety website for official information about UC San Diego's safety policies, procedures, and training.
A list of safety videos is available on the Blink safety portal. Some were produced by Dr. Haim Weizman in the Department of Chemisty and Biochemistry, including A Day in the Lab (A PI's Perspective). The other videos were produced elsewhere.
The Safety Zone blog at Chemical & Engineering News has a of list of lab safety videos (last update: unknown), arranged by topic: emergency response, hazardous waste, pyrophorics, fume hoods, eye protection and more (includes the UCSD videos). The Dow Lab Safety Academy also has an extensive collection of safety videos.
There's also the Napo (Safety with a Smile) film series from European Agency for Safety & Health at Work. "Napo is the hero in a series of animated films that introduce important workplace safety and health topics in a memorable, light-hearted way. The likeable characters symbolises and employee who could be working in any industry or sector."