Creating hierarchy of objects without prefabs

Im coming to Unity from programming in C++ and C# so I know Object oriented programming but not prefabs.

I have created a baseclass and some classes inheriting from this class. Nothing fancy at all. None of theese classes uses MonoBehaviour. So my problem arises when I realised that my baseclass has to have a texture that it should render.

So first question: Can I have this baseclass have a texture that it can render on screen without needing to inherit from MonoBehaviour? If so, how?

As I cant find a way to do so I make the baseclass inherit from MonoBehaviour. Then another problem rises. When I create my objects I can no longer use the "New" keyword. I have to use instantiate(). When i use instantiate() I have to Instantiate an object and not a class.

Question Number 2: How do I create an object without the "new" keyword to use for instantiating?

The best way I can think of is to create a prefab and a public variable that inputs an object from the editor. Im very new to this part of "unity gamedeveloping". I dont like to drag stuff in the editor, it seems redundant and slow. And if I have to do it this way it will take a while to make every object take an input in the form of another object. Thats alot of drag n drop.

But to drag a script into a prefab it apparently needs to be MonoBehaviour so then everything will have to inherit from that. This also seems reduntant when only the baseclass needs the functionality of MonoBehaviour.

Question number 3: The Unity developers are clearly very experienced developers(more than me atlest) so Im assuming there is a positive side to this and I would like to know some of them.