Background checks and training do NOT go with that. This is about Constitution Carry, meaning that the 2nd Amendment (the supreme law of the land) be upheld. That only means that you can carry without a conceal carry permit. What it does not mean is that background checks are done away with. That is because those are handled at the federal level. So if you buy a gun you MUST purchase it from at Federal Firearm Licensed person who by federal law must submit your name for a background check.
The problem with the haplophobic left is that because they don't buy guns they don't know anything about guns or gun purchasing. The Democrat politicians bank on that and tell you all sorts of lies and half truths.
As far as training, I have no idea about that. That would be a state requirement. Most states do not require training. I used to live in Missouri and they required training only if you purchased a handgun and were under a certain age. I don't remember the age but I think it is around 50 years old. If you are younger then you must take a firearm safety class.
Those classes are all taught by the NRA, which the left seems to really want to demonize. The NRA also teaches our military and police forces. They offer all sorts of gun safety classes that anyone is free to take whenever they want. So while the left is running around accusing the NRA of murder, the fact of the matter is they haven't caused any murders but they have prevented perhaps millions of accidental shootings. Murderers typically do not take any NRA training courses and the vast majority of the time they bought their gun on the black market or stole it.
The least used firearm by murderers is the AR-15. All rifles are way down on the list of weapons used by murderers. Knives, hands and feet kill more people than AR-15s. Cars kill more people than AR-15s. But for some reason the left is scared to death by them. They even try to convince you that they are fully automatic machine guns when that is absolutely false.