I think you’re just making your life much harder by creating everything from scratch! Try to use this game engine to your advantage and get the most out of it 
You see, the already implemented and optimized character class will take care of literally everything for you (movement, playing differenct animations, etc.). You will have to implement all of these functionalities from scratch if you go with base classes! Instead, you can very easily disable or extend some of the character’s functionalities and implement your very own behaviors. You can even do these in blueprints!
Now back to why your pawn doesn’t move. It’s because base Pawn classes don’t have any movement algorithm implemented. In fact, if you read the comment for AddMovementInput() function in the engine source code, you will see that it says “Base pawn classes won’t apply movement automatically and it is up to the user to do so in the tick component”. How would you do so? You will need to update bone positions, actor location, rotation, etc. Trust me that’s a lot of work to get a character moving, so don’t make your life any harder and instead take full advantage of what this awesome engine already equips you with So where to start? If you want a character that stands on two legs, start with Character class as your base class (Or even easier go with ThirdPersonCharacter project for C++). If you want a pawn that floats/flies, then go with FloatingPawnMovement component or Flying Template.
For this particular case, the easiest way is the best way 
Hope this helps!
P.S. If you still want to implement your own pawn movement then I suggest you start with this official tutorial here.