Learning to use Godot is more than just learning GDScript. Godot is a game engine, which means it’s a collection of tools designed to help you create games. Scripting is one of those tools.
The easiest way to get started learning Godot is by following the official tutorial. This will guide you through the fundamentals and even includes making a small game.
You do not have to learn Python before learning GDScript. That said, if you do not have any programming experience, starting with a more general purpose language is probably a good idea. The fundamental programming knowledge that you’d acquire in a beginner Python course would be very helpful in learning to make games.
There is no relationship between GDScript and Python. GDScript is a completely separate language. In its design, it borrows much of its syntax from Python, so there is a superficial resemblance. This does make it a relatively easy transition for Python programmers.
Graphics part:
I’m not entirely sure exactly what you’re asking here. OpenGL is an API for programming graphics (ie talking to a GPU). You can read about it here.
As for writing a new rendering engine - this is a massive undertaking. This is currently underway for the 4.0 release, which will support the Vulkan API, and will likely not be finished for at least another year.
Pricing part:
Godot is open source software. You never need to pay anything to use Godot. This is covered on the main page.