6th May, 2016
Spoiler title
Yes, it is possible to switch off physical switches. But the load states will change. The state of the physical switch will not change.
If the router is switched off. Is it possible to control the appliances connected to PERT?
Yes, you will be able to use Physical switches.
Is it possible to control the appliances remotely when internet is not working in the area where PERT is installed?
 No, it is not possible. To remotely operate and control appliances connected to PERT internet is mandatory. To control locally internet is not mandatory but Wi-Fi should work. 

What happens to the appliances if the manual switch is on when the main is power off?
The previous states (before the power was cut) will retain and the same will also same reflect on the mobile app.