Battery Life

no connections were done and kept the device idle on the table.
Is this the scenario were device should last 4 weeks ?

Yes, it should do. Only thing that'd stop it is if devices kept connecting to Bluetooth (but you could even disable bluetooth in settings)

Question is how do i check percentage of battery?

You still have the battery indicator showing in the top right? It's not an exact percentage, but then the percentage you get reported is only maybe 10% accurate anyway.