I would call my prior insurance company (your renters provider) showing the false claim and see how they have it marked. I would also have them send confirmation that the claim was dropped and not paid out.
Unless you notified an insurance company to file a claim or a police officer wrote an incident report of the damage, the repair will not be documented on your driving record or claims history. Insurance companies verify your driving history by looking at your Motor Vehicle Report (MVR) and CLUE report.
Unfortunately the decreasing of points on your license doesn't necessarily translate to lower insurance rates, because the original ticket itself is still on your record. If you happen to have tickets actually dropped from your driving record then that would lead to lower rates.
If you are being charged for a ticket that has already been removed from your record, you may be required to show proof to your insurance company that the ticket has been dropped. If the ticket has been dropped and your insurance company will not lower your rate, you should consider shopping with a new insurance company.
Your best bet would be to request a copy of your driving record from the DMV and see what is listed. If you see something that is not supposed to be on there you may be able to dispute the ticket with the courts.
A non-driving felony conviction most likely won't affect your rate, but it could make you ineligible for a policy with certain companies. Since you are already aware of the incident, you will want to disclose this when you call a company for a quote so they can let you know up front if that will create an issue.