Can I lock the casters so the seat doesn't roll while I'm sitting on it?

Locking mechanism not specified. Test the caster system before relying on it for stability during use — you may want to position it against a workbench or wall for safety.

Are the drawers deep enough for standard socket sets?

Drawer depth is not listed in the specs. Measure your most-used tools before committing — shallow drawers work best for hand tools and small parts, not bulky items.

Does this seat arrive assembled or do I need to put it together?

Assembly status not confirmed. Plan for basic assembly with common hand tools — casters and drawers typically require attachment to the base frame.