I am very curious about graphics-specific programming languages. Can you suggest me something to read about it?
There are a few, including OpenGL (cross-platform), Vulkan (cross-platform), DirectX (Windows, Xbox console), and Metal (Apple). I suggest checking out Learn OpenGL for tutorials on how to use OpenGL.
What are some numerical methods we can use to manipulate and analyze signals?
We will cover all sorts of numerical methods used in graphics throughout the course, just you wait. :-) Computing the norm of derivatives is a nice simple example of a numerical method for detecting edges in an image. More complex methods may include physically-based fluid solvers, particle simulators, or numerical integrators for rendering photorealistic images.