What is the ruling on throwing the pebbles if a pebble hit the pillar and the thrower does not remember after 8 months whether it fell into the basin or not, bearing in mind that exiting the state of ihram requires throwing the Jamrat al-Aqabah al-Kubra, and what is required of him now?

What you have read is correct, for the intention is to make the pebbles fall into the basin. If they hit the target but do not fall into the basin, it is not sufficient. If you are reasonably sure that they fell into the basin, then that is sufficient for you, and reasonable certainty is enough; absolute certainty is not required. However, if you are doubtful about them falling into the basin, or if you are reasonably sure that they did not fall into it, then you must offer a sacrifice (dam) to be slaughtered in Makkah and distributed to the poor of the Haram, if the number of pebbles doubted to have fallen is more than two. As for exiting the state of ihram, it remains valid.