What exactly are the “material conditions leading to gun crime”?
Largely economic and educational, yeah, but also systemic racism and ingrained misogyny. While it's facile--and accurate--to say that Republicans block efforts that would help these problems, the fact is that Democrats often do as well, opting to ban firearms and features rather than addressing root causes. I recall one particular violence intervention program that got cancelled in Chicago by--IIRC--Rahm Emmanuel. And unfortunately, many of the centrist Dems don't really believe in programs that work, like enrolling inmates in college to reduce recidivism.
Why do other countries thar have lots of guns have less gun crime?
Other countries with a relatively high number of firearms also tend to have significantly better social welfare systems, more focus on rehabilitation than punishment in their criminal justice systems, and a lower rate of income inequality overall. If the US had, for instance, the social conditions of Finland, while still having the same number of firearms, I expect that you would see a sharply lower rate of firearm homicides. (Interestingly, Finland has very similar rates of suicide as we have in the US overall. I'm not sure what to make of that. But I also note that all of the Nordic countries seem to have fairly high suicide rates, and all of the Mediterranean countries tend to have quite low suicide rates. Climate and amount of sunlight, maybe?)
Aside from the, the right to keep and bear arms is an individual civil right. IMO, attempts to restrict that right should be subject to strict scrutiny. NYSPRA v. Bruen helped with that, but it hasn't gone far enough. Think of it this way: voting is supposed to be a right. Republicans want to limit the ability to vote in ways that favor them. I would say that this is wrong, and that Republicans need to change the way that they govern or message so that they can attract more voters, rather than trying to make it harder to exercise a civil right.
or the gas station clerk to get a gun pointed at her and told to give up the cash.
...Which you aren't very likely to do once economic conditions have been addressed. Not very many people go out and rob people for the sheer joy of it. Little Johnny shoots Susie because society has taught him that the only acceptable emotion is rage, and he can't deal with his emotions in any other way. Again: address the messaging--about gender norms and expression in this case-- and fix the underlying problems, and then access to the tools of violence becomes immaterial because there's no longer the impetus towards violence. Dems have made some inroads regarding gendered emotional expressions, but a lot of far-right influencers are actively working against those efforts.
parents of shooters bought them guns despite clear warnings
I think that this is probably appropriate in limited cases, such as with the Crumbleys in Detroit, MI, and with the Grays in Winder, GA. In both cases, the parents (father, in the case of Mr. Gray) had credible information from authorities that their child was at risk of harming other people, and both of them gave firearms to their child despite and after receiving the credible information about them being a risk. I would say that, if parents made a reasonable attempt to deny a child access to firearms, or did not have credible information about their child being a risk, then you should no longer be looking at a criminal or civil case. It seems to me that having your firearms locked inside your home or vehicle should be enough to say that you made a reasonable effort, because anyone that takes a firearm from those places knows that they're breaking and entering already.
The desire to make locking firearms up is yet another way of making firearms prohibitively expensive, and functionally denies the right to keep and bear arms to people that can't pony up the $1000+ for a locking firearms container that's even slightly secure.
Republicans need young men to turn out; from what I can see, they are trending conservative. They don't want young women to turn out, because they are trending overwhelmingly liberal.