More on tumbling and lead styphnate dust -
I've found (using lead test kits) that there is no problem with loading the brass into the vibratory tumbler, or the tumbling itself. The gasketed lid contains everything just fine. It is when you dump the media/brass through the separator that things get dusty. So that one step I do outdoors, wearing gloves and a HEPA respirator, and I toss the shirt I'm wearing into the washing machine. The dust is just walnut shell dust, and unless you are filling a room with this dust, I don't believe there is a reason to worry about dust explosions.
More on cleaning fumes -
As long as you have a tight container for any rags, patches, etc. this might be OK indoors, with a fume extractor of some kind running. A solvent-resistant mat might be sufficient to protect whatever benchtop you have, but I'd watch for porous surfaces which could accumulate the cleaning products. Even with a fume extractor running, I'd still wear Nitrile gloves. The thin ones don't compromise dexterity and they are disposable. You might note that latex gloves are not as solvent-resistant as Nitrile gloves.
More on fire extinguishers -
The stuff used in reloading has its own oxidizing agent as part of the compound and all a fire extinguisher is going to do is scatter the stuff all over the room without extinguishing it. In fact, it might happily ignite other combustibles. While there is nothing wrong with having a fire extinguisher around, no matter what you are doing, you should not let it give you a false sense of security. What is important is making sure there are no other fire hazards, ignition sources, etc. in that room. Wiring has to be to code, if you smoke do it somewhere else, etc. And, while the odds are very low, if you have humidity / carpet conditions which lead to static electricity, you should consider grounding your press, metal benchtop, whatever else is around primers when you are handling them. Especially in primer magazine tubes.
.30-06 Springfield: 100 yrs + and still going strong