I would recommend looking at the Unity scripting documentation https://docs.unity3d.com/ScriptReference/index.html

A lot of these questions are answered there. Just use the search in the top right for vector or quaternians. Quaternians are basically an easy way to move objects around the scent programatically like a player walking. They handle the physics that allow it to not behave unexpectedly, such as rotating the frog on it's side. If you don't use them and you try to force it through with Vectors you may run into issues when the player collides with another physics item, such as the wall, or the bird, or the flies. Quaternians handle all that for you taking into account physics caused by other objects. They're really complicated and even I, someone that knows C#, still don't really understand them. And the instructor himself said a lot of developers including him don't fully understand them. They're something people that have advanced degrees in physics would understand though :p

Private variables are variables that can't be accessed outside of their method or class. Public variables can be accessed anywhere in the program. Ideally you want everything to be private if possible and only grant public when necessary.

A lot of the understanding you'll get will come later in the course once you learn C# itself. I personally think maybe the course should be restructured to teach you C# before delving into Unity itself. The videos could be a lot shorter. He spends a lot of time explaining basic concepts such as private/public that could be handled by that course and then he could spend more time on the development.