Hello AJ,
At the beginning of the tutorial he is using a Gamepad to control the character (an Xbox360 controller for example).
That is why you don’t see any signs of a mouse being used.
Regarding the issue of your mouse getting stuck in your play window this is a result of your mouse getting “captured” on play. You can change this setting in the project settings under the input section. Once you are there type “capture” in the search window and have your settings be just like in the screenshot.
The virtual joystick jumping around is known and won’t be addressed at this time.
Hope that helps,