On iOS, do "Automatic Downloads" (incl. Music, Apps, Books, Updates) download on public or slow WiFi networks? If I have "Automatic Downloads" enabled for some or all of the categories (Music, Apps, Books, Updates), then these items will download when available, while I'm connected to my home's WiFi network. 

I enabled these settings recently, so I'm not quite sure on this yet, but if I'm connected to a public network, then will they still download? Because public WiFi networks are often quite slow, so I think the downloads might stall. Is it possible to instead keep these options enabled, but prevent downloads from taking place on WiFi networks that are not my home network?

Or at worst, if a download stalls and I can no longer connect to WiFi again, then is there a way to revert an update that only downloaded halfway? Would restarting my device do the trick?
Yes, they will download even in slow Wi-Fi connections. There is no option to choose an Wi-Fi connection to do the automatic downloads. You can only disable the downloads on Cellular Data on Settings / iTunes &amp; App Store / Use Cellular Data.