A lot of the issues in this part are related to the animation. To make it easier to find the issue, you can dock your Animator window separately from your Game window, and when you are playing in Editor, try to see what animations are running on the Animator window.
Your animation issues may be caused by having incorrect Exit Time or Transition Duration values in your transition arrows.
Problem: Character walks for 2 seconds and then get static
Make sure that the Walking animation in the Animator is set to the duplicated animation file under Assets/Animation, with ‘Loop Time’ is set to true on ‘Walking.anim’. There is a possibility that the wrong animation file is being used.
Just to add on to what Jonathan was saying about docking the Animator window separately from the Game window, it looks like this:
This will allow you to see if the animation is transitioning from one state to another. If not, then you have to check the transitions (i.e. the arrow connecting the animations) to see if your transition conditions, Exit Time or Transition Duration attributes have been set correctly.