Issued plans are the approved basis for construction. If the design changes afterward, treat the change as a documented revision rather than simply building the new version and explaining it at inspection.
Building departments use their own terminology, deadlines and procedures. Treat this as a practical orientation and verify the current rule with the jurisdiction that issued — or would issue — the permit.
Often yes, but changes can require review and approval before construction proceeds.
That depends on the change and the jurisdiction. Ask the inspector or building department rather than assuming a change is too small to document.