How can I remotely control my Android device via PC?
For Online:

try TeamViewer. its a good remote control app from PC to PC and phone to PC and PC to phone.

TeamViewer

For offline:

try AirDroid its good and it worked for me.

AirDroid

If you need just simple commands(enter text, press, perform actions):

adb shell input


text, keyevent, keyboard, mouse, joystick, touchpad, trackball, dpad and more.

Usage:

adb shell input text "Hello"