Ok. I don,t get it. 
I go to the toolchain folder using cygwin and do ./build_toolchain.sh and i get this:

Quote

$ ./build_toolchain.sh
Building and installing to '/cygdrive/c/users/lioł/ndless/ndless-sdk/toolchain/install'...
./build_toolchain.sh: linia 47: gcc: nie znaleziono polecenia
GMP (gmp-devel/libgmp-dev) dependency seems to be missing!
./build_toolchain.sh: linia 48: gcc: nie znaleziono polecenia
MPFR (mpfr-devel/libmpfr-dev) dependency seems to be missing!
./build_toolchain.sh: linia 49: gcc: nie znaleziono polecenia
MPC (mpc-devel/libmpc-dev) dependency seems to be missing!
./build_toolchain.sh: linia 50: gcc: nie znaleziono polecenia
zlib (zlib-devel/zlib1g-dev) dependency seems to be missing!
./build_toolchain.sh: linia 51: gcc: nie znaleziono polecenia
libpython2.7 (python-devel/python2.7-dev) dependency seems to be missing!

"nie znaleziono polecenia" means "command not found" in polish.
What did i do wrong?

Are you running this from cygwin or from the windows command line?
Did you also install gcc and the other dependencies or just php?

1. The links to the files in the one that seems easier are both dead.

You may find this useful: https://github.com/ndless-nspire/Ndless/wiki/Ndless-SDK:-C-and-assembly-development-introduction

2. The more complicated one: Why the heck do i need PHP, openssl and all that stuff to make a compiler running!?     
    Come on! It's a program that translates C language into assembly! Why do i need all that stuff complicated even to
    make a "Hello world!" example? I saw TIGCC, and it has a simple, minimalistic and understandable .exe installer.
    Shouldn't there be something similar for the nspire?

Welcome to the world of open source. Where things require a little knowhow, are very rarely polished, and most developers aren't paid for their time.

If your hardware version is too recent then there is little we can do to help you. You can look at the following sites to see if there is more information about your hardware revision:
https://github.com/ndless-nspire/Ndless/
https://ndlessly.wordpress.com/ndless-troubleshooting/

I have written a chem app that solves Gas Laws. You can find it on my site here: http://www.mason-cole.com/#TI-Nspire

Bit of a necro-post there. This thread is from 2013. If you'd like to post about your projects on Omnimaga I'd suggest starting a new topic and giving some more information about your app.

If you aren't actually emulating the hardware but just the system calls I'd describe your projects more as a compatibility layer (like Wine). If I had time I'd be interested in helping even though I don't have an HP Prime.

You may also want to cross-post this on Cemetech as they have more c++ developers over there.

That said if you need help with higher level planning or want someone to go over your designs and give feedback feel free to post about it here, or to tag me in the github issue/pr and I'll give it a once over the best I can.

Your browser should translate the page from French.

Not all browsers translate pages automatically. Here is a link of the page using google translate

Well this is very exciting

By DOS you mean windows command line? Unless you are still running Windows 98.

There are some IDE's out there, but all I'm aware of have not been updated in a long while and usually make things a little more difficult. I'd suggest just adding build config to your editor of choice (Like Sublime text) and using that.