How can we change the different setting of an beacon with Eddystone Protocol without using any third party SDK, like the SDK's provided by Estimote or AltBeacons. How, for instance can we change the transmitting power/transmitting frequency or the Instance ID of an beacon from our mobile devices (maybe with the help of an app)? Can we change them by using the Bluetooth Manager or BluetoothLeScanner present in Android ? Can it be done or we have to rely on the Beacon manufacturer's SDK to change the values?
No, you cannot change the settings on an Eddystone beacon using any built-in Android apps or OS functions. You need a third party app to do this. For now, this means one of the beacon manufacturer configuration apps you mention.
There are plans to change this. Google has a draft specification for a standard Eddystone configuration service. Beacon manufacturers adopting this spec have hardware that can be configured by any app that supports the standard. So while you will still need an app, you would not need one from the beacon manufacturer. (You could even build your own.)
Still, there are no announced plans by Google to put a default configuration app into Android using this standard. So the need to install some app will probably not change. With the standard, you will just have more flexibility in the app you install.
Full disclosure: I am the lead developer on the Android Beacon Library project, an SDK that is part of the AltBeacon project.