As I understand it there is no 'pilot light' per se. There is a piezo igniter that lights a flame on demand when the water heater senses water passing through it. So the only time there should be any flame at all is when the unit is in use. You should actually be able to hear an audible *click* *click* *click* as it lights when you use it. Turn the water off...flame goes out. Turn the water on...flame gets lit.
They can be ordered and shipped to the store
This hot water heater needs a pump will not work off of gravity
You need pressure on the system to make it work . You will need a pump.
Home depot sells Flojet 12V 2.9 GPM 50 PSI Water Pump . This would do it.
I would recommend using a pump, that way you would have steady pressure.
No way you need a boiler