KQED pays NPR for NPR produced shows that KQED chooses to air. So, yes NPR gets some of that money indirectly. I believe it is possible to support NPR directly via their website.

I sort of do this already with my local public broadcaster. I give to OPB but I also make a separate donation to KMHD radio because I value what they are doing. The money all ends up under the same umbrella organization but I hope the separate stream shows that their listeners value this relatively small part of the overall mission.

It's a mix of both. NPR affiliates pay fees back to hq for the use of national programming based on audience size. Donations to your local station could cover local payroll, equipment, or their payments for national programming.

I see Morning Edition and All Things Considered on KQED's weekly schedule (https://drive.google.com/file/d/1PrFgenUlR9TW8bZJ26LopRObTuB...). KQED pays NPR for that content.

I started donating 50/50 to both my local affiliate and the national NPR non-profit a few years ago. I realized that about half my NPR listening was via the affiliate, and half was via NPR podcasts.

You can also support some of the podcasts directly by joining NPR+.