The better powder for primers is regular strike-on-box matches, a mix of the heads themselves and the red phosphorous from the striker strips. If you get a swage block and some punches you can make the actual metal part of the primer pretty easy with a hammer, although making the little spider thingy that goes in the middle is kinda annoying so if you're DIYing it's easier to make your cartridges with Berdan-style primer pockets with the sticky-uppy bit.

As for the cartridge itself, yeah, brass tube and solder works well for low-pressure stuff like pistol or shotgun rounds. 3D prints work for shotgun shells too. You can also just buy "decorative" dummy rounds (like for jewelry or whatever) and use those, I don't think those are controlled in Japan and all you gotta do is solder over the necklace hole. That's basically the only way to do rifle rounds without a lathe, and considering the tight tolerances and compound tapers of modern bottlenecked cartridges, it's kinda hard to do even WITH a lathe unless you spring for a CNC.