First I connected appliance module to lamp in 1st outlet, it seemed appliance module was OFF.
Then connected it to another outlet it was ON. It's strange. All these happened without using powerline module.
This can happen with X10 stuff. Plug a lamp into a module, assume the module is off and the lamp is on. The lamp will be initially dark because the module is off. Turn the switch on the lamp off and then on, or unplug it from the module and plug it back in again, the module will sense this and turn on for you.
When using Arduino to send signals appliance module is NOT responding to them.
Were the appliance module and the PSC05 plugged into the same outlet for your initial testing? If not, start there. There is no guarantee that the X10 signals can propagate to all outlets in your home or building.
Did your module address and house code match what you were trying to send?