Here is a suggested and performant method to screencast the phone/tablet to your Windows/Linux or macOS computer or a bigger screen connected to one of these machine.

This method also allows some control on the android interface by using PC mouse and/or keyboard.

This method requires no app on the Android device (just some system configuration) and it uses one App (scrcpy) on the computer with the native Android debugger, so the performances are good.

Requirements

1) On the Android device:

• Developer Mode enabled (guide here)
• USB Debugging and (for latest phones/tablets) WiFi Debugging enabled in the Developer options
• On some devices, you also need to enable an additional option USB debugging (Security Settings) (this is an item different from USB debugging) to control it using a keyboard and mouse. Rebooting the device is necessary once this option is set.

2) Get the App on the Windows/Linux/macOS machine:

• Linux
• Windows
• macOS

First Connection

With USB cable

• Connect the phone/tablet to the computer with a standard data cable (not OTG). If the usb cable is correct your should see the phone shared folders on the computer after on the phone you authorize the files sharing.
• Run the file scrcpy.exe
• The first time the phone should ask authorization for the computer access

With WiFi

• First connect the scrcpy app with the USB cable, keep the cable connected and close the app
• Run open_a_terminal_here.bat and on the terminal run this command with the IP address of the phone/tablet:
  scrcpy --tcpip=192.168.1.100
• Next times it should not be required to connect the USB cable first. Important is to keep the Developer options enabled.

Additional

• You may create your own .bat files to open the screencast for your phones/tablets. This will work in case the phone will get assigned always the same IP address.
  Just copy the file scrcpy-console.bat and then you can change the content in something like:
  @echo off
scrcpy.exe --tcpip=192.168.1.xxx --pause-on-exit=if-error %*
• You can record a video using some scrcpy option. Check at this link for more information.