I'm looking for a good book (idiot proof) for learning all the magic behind computing matrices, quaternions, euler angles, orientation in 3d space and more...
Book needs to have examples and solutions of typical problems.
I have tried several books/articles, but whenever I find my self in a situation where I have to compute something it doesn't end well.
It sounds like you could use a basic education in the fundamentals of vector algebra/vector analysis.
Find a good basic vector algebra/analysis text and/or (better yet) attend a class or find a tutor for the subject. If you're determined to learn it and you are looking for problems, then there is probably a Schaum's outline edition out there you would find useful. You do not have to go too far into the weeds with vector analysis, though.
With a basic knowledge of vector algebra, you should be able to get your head around transformations, rotations, and quaternions.
You might also find this post useful: Is a full semester of Linear Algebra really needed if I want to specialize in computer graphics?