I have two questions to ask.
If I want to code in ARB, what are the prerequisites I need to write the code?
I have been using OpenGL and DirectX lately. I want to compile and run the ARB code. What compiler should I use to compile and run the code?
It's no longer advised to code directly to assembly. It was important during Nvidia FX5xxx/Radeon 9700 era. A very long time ago. Now all shaders are compiled by drivers to extract max performance out of the platform.
Use OpenGL shading language, or use Nvidia Cg to generate an assembly from C++ like code.