The training course seems reasonable on the surface, but what about poor people? Aren't you effectively limiting the most in danger segment of the populations ability to protect themselves by forcing them to pay for a class, take off work, and actually go to classes? As for the waiting period, this is already law in most states.
By federal law everyone has a background check on them when buying a gun from a dealer. As far as your mental health evaluation, 1/5th of the entire country is on at least 1 psychiatric medication. Even if the mental health evaluations start off as reasonable, you know damned well it won't stop there. It could easily include anyone on any psychiatric meds, then anyone with depression, or anxiety, or even family history of issues.
Using the excuse of "mental health evaluations" you could effectively disarm more than half of the US population. I agree crazy people shouldn't have guns, but the issue is not if crazy people should have guns, it is how do you effectively enforce this is a in REALITY without stripping the rights of millions of others as well. Additionally perhaps instead of treating the symptom of gun violence, maybe we should be treating the USA's crazy person problem instead. The mental health care options in the US are almost nil unless you have the big bucks to afford it, which IMO is one of the primary causes of this issue along with certain types of psychiatric meds.
The mental health check isn't an issue of whether anybody with any mental illness shouldn't be able to have one, but where to draw the line. Maybe people with depression, bipolar, etc would be able to get one, while people that are more 'up there' with schizophrenia, psychosis, etc can't.
You are likely far too trusting of your Overlords on the bolded above. You presume they have good intent - I presume that they don't, often times.
Further, mental illness is far less precise than these words imply. And it wasn't too long ago that actual, certified Mental Illnesses included -
Homosexuality
Nymphomania
Certainly you don't want THOSE PEOPLE to have guns. Do you? Wait, are we more enlightened today? Smarter? Better informed? More scientific?
Might want to think those things over a bit, lol....