A lot of that is stuff that's been on the anti's wish list for a while, and a lot of it is just wishful thinking, or at least, stuff that they haven't thought all the way through.
Like the stalker thing - either the stalker has been convicted of a felony crime, and thus is already ineligible, or not. Since SCOTUS has already said the RKBA is a fundamental right, you can't just go taking it away for misdemeanors (yes, I'm looking at you, Mr. Lautenberg.)
Same thing with their so-called "terror gap" - there's huge due process issues with that, especially "suspected terrorists." I think Schumer at some point was trying to get everyone on the the No-Fly list put on a "No Buy" list, until the due process issues were pointed out.
And unless the Feds are providing funding for reporting state criminal and mental health info into the NICS database, they'll run into the unfunded mandate problem. SCOTUS has already said that Uncle Sam can't just force the states to incur expenses without giving them funds to pay for it.
And "treat gun trafficking as a serious crime" is something you'd probably get agreement on from the NRA, GOA, SAF, and most gun nuts. For whatever reason, probably having a lot to do with bureaucratic incentives, law enforcement agencies don't seem to make it a priority. (Unless they've got other motives, as in FnF.) If I had to guess, I'd say it's probably a high work/low reward kind of thing. Local agencies don't have the resources, and may or may not share info with the Feds, if the Feds are interested. For the ATF, it's a lot easier to ding FFLs for paperwork booboos than it is to invest lots of resources in gun running investigations that only net a few convictions.