The Schrödinger's cat is both dead and alive, until an observation is made.
This is a very misleading ( and cruel) gedanken experiment, using a cat as a detector for the quantum mechanical behavior of decaying particles.
There is no way one can tag which particle will decay, each has a probability of decaying, and the cat experiment stresses the probabilistic nature of quantum mechanics and confuses macroscopic perception with microscopic reality, imo.
Macroscopic objects have to be treated classically, composed as they are of order 10^23 wavefunctions which at the cat level are incoherent and therefore classical in behavior.
There is no way to distinguish between interpretations experimentally. They describe the same data. If they do not, they would not be called interpretations. An interpretation which did not agree with all microscopic measurements would be falsified and no longer be in the list.
Edit, after edit of question:
Is it the same case with Copenhagen interpretation? Does it really say anything about the world?
It uses the mathematical model on which it is based to describe existing experimental data and predict future behavior. Up to this time it is continuously validated even when extended to new kinematic regimes as with special and general relativity.
The other interpretations in the list either have their problems (cannot be extended) to new kinematic regimes as with the Bohm theory, or are too complicated conceptually to help in developing intuition in the microcosm data, and thus main stream physics teaching does not use them.
In this sense it is discussing the complexity of mathematical language.
It is possible, (as with the case of Newton's "particulate nature of light") that future experimental data in new kinematic regimes might pick another interpretation than the C one for new data from higher energy regimes or unthought-of at the present boundary conditions. This would not invalidate the usefulness of the C interpretation's simplicity in the existing data. We still use classical mechanics in the proper regime.
Is it possible to understand quantum theory merely through probabilities, without the 'self contradictory' descriptions?
In mainstream physics experience, yes.
The simplest way to understand the double slit experiment , one electron at a time, that shows that at the quantum level the electron is a quantum mechanical particle, is the Copenhagen interpretation, with probabilities.
In the top frame the dots are the footprints of electrons in the experiment "electron scattering off two slits of given geometry". It is what is expected of a particle, a specific signal at (x,y,z). The gradual accumulation though shows the interference pattern of a wave. There is no self contradictory description. Just the discovery that at the microcosm particles are not billiard balls, which have a random probability distribution when they scatter. Electrons have other attributes, which the C interpretation describes by using probabilities of interaction with the complex conjugate square of a specific wavefunction, of specific differential equations(,called wave equations because of the sinudoidal solutions they give) in the given boundary conditions of electrons scattering off two slits.