There aren't stats on what percentage of gun owners own their weapons legally but presumably yes legal owners outnumber illegal ones.
There also isn't much on what percentage of illegal shootings are done with illegal guns. However what there is does indicate that most crimes and murders involving guns are done with illegally-owned firearms. Mass shootings are overwhelmingly done with legal guns however.
https://www.statista.com/statistics/476461/mass-shootings-in-the-us-by-legality-of-shooters-weapons/
Whites and rural people do have higher levels of suicide and gun suicide.
Most mass shooters are white:
https://www.statista.com/statistics/476456/mass-shootings-in-the-us-by-shooter-s-race/
https://nij.ojp.gov/topics/articles...masses-details-half-century-us-mass-shootings
Of the 172 individuals who engaged in public mass shootings covered in the database, 97.7% were male. Ages ranged from 11 to 70, with a mean age of 34.1. Those shooting were 52.3% White, 20.9% Black, 8.1% Latino, 6.4% Asian, 4.2% Middle Eastern, and 1.8% Native American.
Obviously yes they are mostly in built-up areas.
16 million 1st time gun owners in the last 2 years sounds a little high.
https://www.nssf.org/articles/nssf-retailer-surveys-indicate-5-4-million-first-time-gun-buyers-in-2021/#:~:text=NEWTOWN, Conn.,the first time in 2021.
The National Shooting Sports Foundation® (NSSF®), the firearm industry trade association, revealed that at least 5.4 million people purchased a firearm for the first time in 2021. Nearly 30 percent of all firearm purchases last year went to new gun owners, based on NSSF’s retailer surveys and adjusted National Instant Criminal Background Check System (NICS) background checks.
Retailer Sales Survey
That figure is a 10 percent decrease from the 40 percent of first-time gun buyers revealed in similar surveys in 2020. More than 21 million background checks were conducted for the sale of a firearm then, with over 8.4 million of those estimated to be for those buying a firearm for the first time.