Can these sorts of programs exist in every Turing-complete language?

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Published on 2010-04-08T15:13:46Z Indexed on 2010/04/08 18:33 UTC
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turing-complete

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language-agnostic

In every Turing-Complete language, is it possible to create a working

Compiler for itself which first runs on an interpreter written in some other language and then compiles it's own source code? (Bootstrapping)
Standards-Compilant C++ compiler which outputs binaries for, e.g.: Windows?
Regex Parser and Evaluater?
World of Warcraft clone? (Assuming the language gets the necessary API bindings as, for example, OpenGL and the WoW source code is available)

(Everything here theoretical)

Let's take Brainf*ck as an example language.

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