Gosh.
Firstly it's rather hard to give any solid advice unless we actually know what you're trying to do.
Are you trying to make a 4D game? A 4D modelling program or raytracer? Or do you simply want to make a program to calculate statistics of certain 4D shapes?
To try and answer your questions, though...
1. I think what you mean is "how do you compile/debug a program you are writing?". There are lots of different programming languages and they all come with their own compilers and some of the popular ones even have IDEs. I would personally recommend the
C programming language and the
Code::Blocks IDE, which includes the
mingw compiler.
2. Wikipedia will give you a start. After that, you're generally looking at Google.
cplusplus.com has a very nice reference for the most common library functions, which work in pure C as well as the titular C++.
3. If you want to make a website you'd need to learn XHTML and preferably CSS and PHP too. Though if you only want to post your research somewhere I suggest creating an account on the
Higher Dimensions Database and contributing there. One wiki can often be better than dozens of individual research sites if there's enough content on it.