California has every single law you asked for except an insurance requirement, and it still happened here. I seriously doubt adding an insurance requirement would have stopped this.
"We should be doing the same for guns at a minimum."
California already requires a license, with an associated test to purchase a firearm. The license is called a Firearms Safety Certificate. It has been required here for years.
The license needs to be renewed every five years, and you must pass the test again in order to renew.
It used to be called the HSC for handguns, but a few years back they changed it to the FSC for all firearms.
" If your gun is stolen and used in a crime you would share in the liability, - especially if your gun was not stored in a safe manor. "
Safe storage in a secure container is the law here. It is a misdemeanour with loss of firearms rights for 10 years if you are caught not storing it correctly. Additionally you are liable for any crime that was caused by your firearm if it was not stored properly and an unauthorized individual got a hold of it.
"A gun should have a title associated with it that gets transferred even in the event of a private sale"
All guns must have a serial number on the frame. The serial number is registered to the owner and the registration is transferred even with a "private sale", inheritance, or any other legal transfer.
As an aside, there are no "private sales" in Californa. All sales must go through a licensed gun store. Even gun shows.
The only exception to this is "Curio and Relic" firearms, meaning the gun 50+ years old, and they have to be on a list designating them as such. Usually to get on this list it means they no longer make ammo for the gun. Last time I looked, there was only a handful of times a C&R firearm was used in a crime since they time they started keeping records.
"gun dealerships should be expected to perform due diligence before selling anyone a gun"
California requires a background check on all persons, they must also wait 10 days and posses a valid FSC before taking possession of a firearm. The purchaser must show two forms of ID, one must be a California state ID (or driver license) the other must have your address on it. The address must match your ID. California also requires a safe handling demonstration where the buyer must show they know how to safely load, unload, and operate the safety of the firearm they wish to purchase. The firearm shop is expected to do these checks.
The owner of the gun shop faces criminal liability (meaning go to jail, not just fines) if the shop does not follow the law. Some gun shops were shut down in the southern part of the state recently due to the owner being "not good".
"More to your point, certain kinds of mental illness would lead to the loss of gun licensure and if your mentally ill son shoots up a mall with your guns, you will be held responsible. "
This is already law here. A 5150 (going nuts and being admitted to the hospital for observation) results in an automatic 10-year loss of guns rights.
The state department of justice has a group called APPS, (that had some growing pains when they first started) that goes out and confiscates the firearms of people who were 5150ed before they get out of the hospital.
Any persons who provides a firearm to an ineligable person is guilty of a felony. If you give a gun to your crazy kid and the cops find out then you go to jail, even if your crazy kid didn't shoot up the mall.
More firearms laws won't fix this. All they will do is annoy the folks that have firearms as their hobby.
We need a culture change where crazy people don't feel that killing a bunch of people is the solution to their problems.