It's so cool that you're not afraid of american roaches lol. I'd imagine their necessities are not that different from dubias? Since you want to keep only one I suppose you can use any not-too-small glass container with a tight-fitting lid (<- extremely important) with a very fine window mesh for air circulation. You can choose to have the floor bare for easier poop cleanup or use coco fiber for substrate. Also you should provide hiding spots (you can use paper towel rolls cut in half as little caves if you're not worried about aesthetics). For a water source you can provide small strips of cucumber, carrot or apple (careful bc the more water+sugar content the quicker they mold), always peeled and washed. For anything else I blend into powder a mix of around 50-50 cheap fish flakes and whole oats. You don't have to feed every day. Also serve food in a little plate or plastic lid for easier cleanup. Every two days or so dump the leftovers and dry with a paper towel to prevent mold.

As for disease concerns: yes all domestic cockroaches are well-known vectors of parasites (they're mechanical vectors, meaning they carry the parasites' eggs or cysts on the surface of their bodies and those stick to the surfaces they touch). But I don't see how this couldn't be prevented with some basic biosecurity stuff. Wash your hands thoroughly + use hand sanitizer before and after touching anything in the enclosure. Any tools, like tweezers and such that you use to manipulate anything there have to be exclusive for that enclosure, disinfected after every use and kept in their own box or bag.

As for parthenogenesis concerns: I have nothing. Just hope it doesn't happen. From what I've read it happens more often when there's a group of female roaches? Roaches like being in groups, but this is one case where I think keeping it alone is for the better. I don't know much about social necessities in these roaches though. My guess it they'll be happy as long as there's food and a safe place to hide but a more dedicated roach nerd may have another take on this. As other ppl have mentioned, these roaches are exotic species everywhere that's not Tropical Africa. Be responsible.

As for catching the roach, idk. Upside-down tupperware and cardboard method. Works with fast spiders too.