Newbie, looking for input on hooking up switches/outlets

I just got the Vera Edge for Christmas and also a Wireless switch (on/off) model GE12722 Z-Wave. I am looking to install this on a On/Off, non dimmer hallway switch. My house was built in the 50’s and when I went to install the new switch I found it only had 2 wires, 1 black, 1 white. I tested the power and the black is hot even when the switch is off and the white only when the switch is on.

  1. Will this model light switch work with my current electric or is there a simple way I can make it work? If so, where does the “white” wire connect?

  2. If this switch won’t work for this setup, can anyone recommend one that will?

  3. I have 2 rooms with this same wiring config on the light switch but but have a ceiling fan/light combo that are both either off or on depending on the switch and the pull strings hanging under them. What light switches are recommend for that type of setup?

I am a computer programmer so electricity isn’t my strong suit, but I have a friend who will be assisting but I want to make sure I buy the correct “tools” for the job.

Thanks in advance