No; to be honest we'd rather not release it until we have something that's pretty polished, since there's not much point in having people beta test something with a lot of obvious bugs we already know about. (would waste users' time filing reports and our time checking them against our bug database)
Depends on when it's ready and on how quickly Apple addresses the bugs in iOS 13. Honestly the extreme bugginess of the first few iOS 13 versions has more *more* inclined to require it if possible, since that way we can require 13.1 or 13.2 or whatever the first non-terrible version of it is and not be stuck supporting the in-between versions of iOS 13 too.
Not officially, but some users have had success running our Android app in various emulators on desktops, and newish Chromebooks support running Android apps officially through the Play Store so if you consider those to be 'desktops' that would be a desktop version.
Also, we are hoping to launch a macOS app later this year when Apple releases a macOS update with their new "Project Marzipan" allowing iPad apps to be easily recompiled to work on Mac.