Housing:
Any large plastic tubs or tanks will work for these, size purely depends on how many individuals you have. I'd say you can fit about 6-10 adults per gallon depending on the available surface area, small nymphs can handle much more crowded conditions. If things get too crowded, they'll probably just cannibalize each other until they've reached their preferred population size.
These assassin bugs have an extremely painful venom, so while they aren't the best escape artists, an airtight lid is definitely recommended.
For adults and nymphs, I'd personally recommend a bare bottom enclosure with plenty of hides, preferably eggcrates, cork rounds, etc., this makes feeding easier, especially if you want to use burrowing roaches as feeders, (Pycnoscelus spp. for example make great feeders for this genus). Some verticality is appreciated, especially for when the subadult nymphs molt into adults, if the hides and the enclosure are too short, mismolts can occur.
They get almost all their moisture from their prey, so a moderately ventilated, dry enclosure won't bother them, though I do suggest misting them lightly every couple days.
Eggs need to be kept moist though, and should be kept in deli cups with a thin layer of moist coconut fiber, and the cups should have at least a little ventilation.
Some people keep all their life stages together, keeping adults and nymphs together in an enclosure with humid substrate and lots of hides, letting adults lay eggs in said enclosure, which works for keeping a small colony. However if you want hundreds of Pystalla, you'll want to be isolating the eggs from the adults' enclosure, which is another reason why I suggest a bare bottom tank for adults, (we'll go into more details in the breeding section), and you'll also need to keep the resulting nymphs in a different enclosure, so the adults won't eat them.
Diet:
Pystalla are strict predators, and only eat live invertebrates. Even the smallest of nymphs can take on prey nearly their own size, and sometimes several Pystalla will team up on one prey item. Soft bodied prey like crickets or cockroaches are suggested as feeders, however they have to be fairly active, as Pystalla seem to sense prey by movement, so prey that plays dead usually makes poor food for these assassin bugs. However, prey items that can climb smooth surfaces are not good feeders for Pystalla, as they will almost certainly escape their grasp.
Additionally, while they will go after prey nearly as large as themselves, they will also go after smaller prey items, so they aren't too picky when it comes to size. Also, Pystalla seem to prefer grabbing their prey from above, so take that into consideration when designing your enclosure.
They may suck at fruits you place in their enclosure, but that is pretty much purely a hydration method, they aren't actually sucking the fruit for nutrients.
Temperature:
While they seem to survive and grow anywhere from 70-85F°, I found that they bred best in the 75-85F° range.
Breeding/Life cycle:
Adults live for roughly 8 months, give or take, and females lay dozens of eggs during their lifetime, about 5-10 a week. These eggs take 1-2 months to hatch, and the resulting nymphs take 6-7 months to mature.
Now what I like to do when breeding these is to keep the adults in a dry, bare bottom enclosure, as they usually won't lay eggs without a moist substrate, such as coconut fiber, peat moss, potting soil, etc. Then once or twice a week, place a shallow deli cup with half an inch of moist substrate into their enclosure, leave in in there for a day or two, and take it back out, the females should have laid several eggs within the moist substrate.
Alternatively, you can just take a big eggcrate that's got a bunch of adults on it, and place that in an enclosure with a thin layer of moist substrate for a day or two, then put them back in their bare bottom feeding enclosure, they should leave behind plenty of eggs in the substrate.
I then suggest digging through the substrate to remove the eggs, and place them in their own deli cup. Once they start hatching, remove the nymphs and move them to their own enclosures, preferably keeping nymphs of the same instars with each other. L1s and L2s can be kept together safely, but an L3 nymph might see an L1 as food. Eventually though you'll have so many of them that cannibalism won't be an issue, but when starting a colony it's better to be safe than sorry.
Overall, these assassin bugs are actually pretty easy to keep and breed, and it's not hard to get hundreds of them using the methodology described above!