Support for mental health: you want to start scanning everyone for health issues? Lots of people will pass those tests with flying colors and still end up shooting people.
Shrink the gap between rich and poor: don't see what this has to do with it. Lot of poor people out there don't have guns or issues...
FBI doing their job: you're probably blaming them for this ONE occasion where they didn't react and admited to it...
Background checks: 100%
Restricted permit: this doesn't solve anything if anyone can just get a permit.
It's not about screening the entire population it's about having services readily available when they are needed. Instead of having someone that's maybe on the edge wait for months on a waiting list jumping through hoops and not being able to afford help.
Gap between rich and poor: creates resentment, fosters envy (the I'm going to get mine at any cost mentality, that drives criminality to be acceptable). Canada isn't perfect but we mostly don't have as much third world level poverty on our streets and in our communities as the US does.