A failed inspection usually means the inspector identified work that needs correction or could not verify a required condition. The practical next step is to understand the inspection note, correct the item and request reinspection when ready.
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.
Usually no. It generally creates a correction and reinspection step, subject to the city's rules and permit status.
Some jurisdictions charge certain reinspection fees in some circumstances. Check the responsible city's current fee policy.