Privacy laws are in place for a reason. They are also largely irrelevant because due process is the concern, not the lack of information. The court system must be involved in the restriction of rights. And it is. A person that has been judged unfit or involuntarily committed to an institution is barred from owning firearms. For life. This is a reporting issue, it shouldn't be an excuse to erode privacy and due process rights.
Safe storage laws are also both unenforceable and ineffective, particularly within your paramaters of reducing gun homicides and not negligent discharges. Not to mention, SCOTUS has declared them unconstitutional. If someone is the victim of a crime, say having their gun stolen, safe storage laws actively and literally blame the victim.
Now, don't get me wrong. I support safe storage. I support the free trigger lock campaign, I support local sheriffs offering free trigger locks, and I support tax breaks, or ideally credits, for purchasing safe storage equipment. Safes are expensive, particularly effective ones. The "gun safes" you see at stores literally legally aren't safes. They're "residential security containers" and are only slightly more secure than a $20 lockbox from Walmart.
As for medication, yes there are side effects. I would support actual scientific study connecting specific medications to specific events of violent behavior and going from there. A little picture saying "these dudes were on drugs" isn't a good enough reason to villify something that helps millions of people.
Any illegal drug use and any abuse of legal drugs already bars purchasing a firearm. Good luck identifying and restricting someone that smoked weed before they went to the gun store.
We already have background checks for every purchase through a dealer. Mandatory renewal simply burdens the existing system. And how do you enforce it?
Licensing is a massive system with very little return. The people willing to obey that are the least likely to cause an issue, let alone that it's a poll tax and a literacy test rolled into one on a Constitutional right.
Focus on the cause of violence, not the already restricted tool that also happens to be specifically protected by the Constitution. Reworking drug laws, violent offender sentencing and release, and domestic violence convicts prohibited possessor enforcement addresses about 97% of the basic motive for gun homicides. You're trying to solve 1% of the issue with solutions that impact 100% of lawful gun owners instead of with solutions that address the actual criminals responsible for almost all gun homicides.