A:Answer "Does it have a on and off switch for brush roll?"
Essentially, it does. There is a switch to toggle between carpet and hard floor. If it is on the hard floor setting, the brish roll will not activate. Also, you have to angle the vacuum cleaner backwards when it is on carpet setting to activate the brush roll.
"Can it be used on luxury vinyl tile?"
Don't know.
"Will the under appliance wand work with it?"
I don't see why not. It has a wand and I have used it under the refrigerator. It got a lot of dust out.