Keil uses a version of arm-gcc.
But also a modifed version of gcc if I am not wrong..

I suggest you to learn how to compile and how to use gcc. Then, why not, you could learn ARM Assemby Language (of course you need to know the machine Assembly language for the architecture you want to compile for, if you would like to develope a new one [*]).

[*] Good luck! : )

 

One question that hasn't really been explored is: Why are you wanting to do this? If it is to target C at a processor that no compiler exists for, then that is a reasonable thought and almost certainly an unreasonable goal (especially for you, vead, given your history of trying to bite of way more than you are ready to chew). If it is to understand the basics of how a compiler works, then that is a reasonable goal, but probably an unreasonable language to choose, at least first off. You've gotten some good suggestions. Another is to look at the Nand2Tetris project that will walk you through an reasonably complete computer system starting with NAND gates and through the entire architecture, writing an assembler, writing an intermediate-language virtual machine, writing a compiler, and developing an operating system library. Details can be found in my blog.

 

Using a Windows Visual Studio IDE and just writing a very simple assembler- where you can insert a few kinds of instructions into a list view, then "run" the program and "visualize" the results; would be demanding already.

You'd have to deal with pecularities of Windows messaging, timers, output to Gadgets in a Form, allocating and administrating memory, and maintaining files.

It's often useful to know how to do that, before taking a flight through all technology to write a compiler + an IDE as well and a debugger too.

 

I think the OP needs to start learning something in terms of programming first. A compiler is a pretty ambitious first project. Once he learns his first programming language, he will have a better idea of "how much he doesn't know." Then he can reassess if a compiler is a good project or not.