Reading some science history, Werner Heisenberg and Bohr created the Copenhagen interpretation, but what I didn't get is how can we connect this interpretation to Schroedinger's cat and the double slit experience? Are they confirming Heisenberg and Bohr's work?
If you really want to understand how QM formalism relates to the Schroedinger's cat and the double slit experiment, you should study a QM textbook.
To answer your question in a simple way:
The double slit experiment is indeed consistent with the Copenhagen interpretation, in the sense that wave mechanics predicts the outcome of the experiment correctly.
On the other hand, Schroedinger's cat is not really an experiment, it is just an illustration of something Erwin Schroedinger did not like about the Copenhagen interpretation, the collapse of the wavefunction during the measurement. Being an illustration, it can't really support or falsify the interpretation.
Maybe I should read Schrödinger's original article first, but I think its purpose is more to highlight deficits in the way some proponents of the Copenhagen interpretation presented that interpretation, rather than to highlight any fundamental problems in the interpretation itself.
You are simply not supposed to ask questions or talk about any unobserved intermediate state. This quite reasonable restriction becomes unintuitive in case the time between two successive observations significantly exceeds the coherence time of the system. An unintuitive situation can arise by coupling a system with a very long coherence time (the supposed radioactive decay in this case) to a system with a very short coherence time (the cat in this case). Because the exponential distribution is memoryless, "virtual" intermediate observations wouldn't really change the predicted probability for the "final real" observation. The consistent histories approach may be used as a clarification of the Copenhagen interpretation that allows a more intuitive understanding of such situations with different time scales.
But the fact that such a simple example like Schrödinger's cat can generate so much confusion points to a much more serious deficit in the presentation of the Copenhagen interpretation. If this interpretation is sufficient for understanding everything that needs to be understood about about quantum mechanics, then it should also be presented in a way that people realize that they understand everything that needs to be understood. Other mathematical theories have similar problems (take for example intuitionistic logic), but here the proponents at least realize that there is a problem which can only be addressed by the proponents themselves.