Z-stick offline

Using R Pi3 and Z-stick, Can light switch be turn off / on, if internet or internet connection hoes down? Clint

You don’t need internet access to switch lights on or off via openHAB as long as you are in your local LAN (for example through wifi).
As soon as you are away from your home and your local LAN you need something like f.e. my.openhab to switch your lights through the internet.

Thank you, SiHui. I am trying to automate a evaporative cooler. Using
Raspberry Pi to control switches. Pump on 1 switch. Motor(blower motor) on
other switch. Program so 10 minute delay between pump on then motor comes
on. Using Python3 language to take temperature sensor input & turn on
switches 10 minute delay between pump on then motor on. This allows water
to wet pad before air blows through. Z-WAVE outlet can be controlled by
wi-fi from Raspberry Pi? Thank You SiHui.

Yes.