They're all wifi and cloud based. They won't connect directly to hubitat (they aren't even in the Hubitat compatibility list). That said there is a beta tuya integration in Hubitat package manager. Also here
No, wifi devices stay on the network that you put them on. The issue with Tuya wifi is that it sucks. I do have a lot of Tuya devices but they're all zigbee and thanks to @kkossev they work very well on Hubitat.
The way Tuya Wifi works is phone>>cloud>>reverse tunnel to device.
The way hubitat works with anything wifi that uses a local API is
Command from whereever>>device
The tuya integration I pointed out above uses
Hubitat>>cloud>>reverse tunnel to device
Sadly a lot of crap like Tuya wifi is foisted on the public.
Now, one thing you could do is if you have google/alexa/apple (homepod/homepod mini or Apple tv) is to attach your tuya account to those then use the built in Hubitat integration with virtual switches to control the tuya wifi device.
