Stones. It really depends on where the stone is. Some stones last for years and never cause any issues. Others, especially those that obstruct the ureters, can cause blockage to the outflow of urine and result in kidney damage. It can start causing scaring of the kidney in a few weeks. If both ureters are blocked, you can go into acute renal failure in a few days (usually temporary).
It may. Sit in the kidney and never cause damage. However, if the stone obstructs the urine draining from the kidney and doesn't pass it can, over time, cause kidney damage. Infected and obstructed kidneys can become damaged quickly.