A good starting point might be Perceptron, then Hopfield and then FeedForward. And in the mean time you will learn different training and error calculation algorithm like- hebb's rule, delta rule and after that, Backpropagation.
Don't worry, your english is as awesome as your explanation I am getting a hold of this, but I need to experiment a lot before I can understand it clearly. But you answered my question and that's enough for starting experiment without any confusion.
If you don't know OGL or DX, please don't go to that route. You will eventually get frustated. Even when you are a very good C++ and OGL/DX programmer, you need to know about scene graph management, bsp trees, 3d model importing, shading and many many more things to make an FPS. Like the others said, don't go this way.
Note: But if you want to look at the amount of knowledge needed to make an FPS. Just go to ID Software's website and download any of their Doom or Quake source code. You will know why we didn't recommended it.
A game engine is nothing but a library with or without user interface. So if you have a game in your mind that you would like to make, then structuring the common code from the game specific code gives you your own game specific game engine. You can then use those common code and make another game and obviously some new (no matter how small) common code will get included in your engine and it will eventually be extended.
But as you mentioned, if it is just about DX11, then you should be better off by not going to the above mentioned path, because a engine is about everything residing in a game, not only the graphics part.
I actually advice you to start with Unity and have a c# reference book by side. like- deitels C# how to program, and then you come up with a fairly small game idea, try to get your feet wet, when stuck search for it until you find it, in the reference books or in online unity tutorials etc. in this way you will get a good idea in which direction to go and what to do. Good Luck