I'm not sure you can ever reduce the negative impact of anything onto itself.  You can try to change society's perspective on violence and the worth of human life.  Guns are just tools much like a knife is a tool.  If used in the proper paradigm hey can have a very positive influence.

Removing the irrationality of religion would be a first step in understanding that human life is not to be trivialized.  Also moving away from a materialistic society would reduce poverty and in turn reduce violence.  Guns aren't the only thing that kill people, they just make it easier.

As to the first recommendation I believe that most states have some kind of similar law or if not a lawsuit could be pressed using a general negligence statute. If you leave a loaded gun laying around and someone hurts themselves with it, you will be held liable. I see no reason to make a federal law that duplicates state laws already in existence. 

As to the second I don't see it doing anything useful. Already you are required in most states to have a basic safety course to either get a permit to carry in public or to use a firearm for hunting. Since many (most?) firearm accidents occur among hunters who have taken this safety course it is obviously not a cure-all against accidents. Probably because a government course on firearm safety is exactly as useful as a government course on driving safety. I highly doubt that either does shit to actually prevent accidents. I wouldn't really go through the effort of opposing it as I have already taken advanced hunting safety courses and have taken handgun courses far more intensive than those required by the government so personally it wouldn't matter a hill of beans to me. I do think that such a program at the federal level would simply be a waste of a bunch of money and involve federal bureaucracy which would probably lower the quality of the safety courses currently required in most states and probably not save a single life (and perhaps cost lives since the federal program would almost certainly have lower standards than those required in many states).  

The federal government has proved time and again that it is completely cumbersome at handling these types of things. It is huge, slow moving and out of touch. I don't think federal laws are the answer to helping anything. Look at the complete and utter failure of "No Child Left Behind" The sledge hammer that is federal law simply is not useful for pounding in a two penny nail. 

As I suggested before in one of the many recent gun control posts, I do think it is completely appropriate for a person who fails to secure their firearms to be liable in a civil lawsuit if one of their guns is used for crime. If you allow someone access to your guns and they commit a crime you should be at least partially liable. If someone steals one of your guns you should be (and you are in most states) required to immediately report the theft. 

The reality is that the hysteria around guns is hysteria. The majority of people who get shot by guns are people committing suicide- no amount of safety programs or holding the gun owner liable for their self injury is going to prevent them from deciding to put a gun to their head and pull the trigger. Maybe you could address that problem by attempting to improve the mental health system in our country (which is currently extremely pathetic). Perhaps if you had steeper penalties for gun owners who have a mentally unstable relative off themselves it might make a difference- but probably not much. Really, if the prospect of their own child committing suicide with the gun wasn't enough to make the parents secure it, is the threat of jail time after that kid commits suicide going to make them? 

Sure, safety training is important. And I have no problem with states increasing training requirements for anyone getting a carry permit or hunting license. Really, in many states the required minimums are fucking jokes. I just don't think that the federal government is going to do a better job and most likely will do a worse job. (Since they do a worse job at absolutely everything else they do) Safety courses offered by organizations like the International Hunters Association, NRA, National Shooting Sports Foundation, National Wild Turkey Federation and the United States Sportsman's Alliance offer courses that are far superior to basic state mandated ones.

Want to improve firearm safety? Allow these types of organizations to provide courses in middle schools, high schools and colleges around the country. They have hundreds of thousands of qualified instructors who are willing to volunteer their time. Unfortunately, most schools will not allow firearms on school property so safety courses cannot be taught on school grounds and when these organizations attempt to reach out to schools and offer free safety programs they are told "NO! ARE YOU CRAZY!!!! WE CAN'T HAVE FIREARMS IN A SCHOOL YOU EVIL NRA NUTCASE!!!!". They are usually forced to hold their courses at off campus locations, and in many cases not even allowed to advertise on school grounds which means they are less accessible to many students. IMO, whether you are ever planning on hunting or not, whether you ever will own a gun or not, having a basic course in how to safely handle a firearm is never a bad thing. We don't need some huge government bureaucracy, we just need the government to get the fuck out of the way and allow these organizations to provide the courses. If you want to improve firearm safety in your area, you don't need a federal law- go to your local school board and ask them why firearm safety courses are not offered at your local schools.