If in the quantum world reality is just based on observation then why molecules (with electrons and protons) are real? If in the quantum world reality is just based on observation then why atoms and molecules are real?
I mean, it is said that when a quantum particle is not observed it's neither spinning up nor down (if I understood that correctly), and from what I understand everything has its quantum particle, and so, why molecules down to electrons and protons have a predictable behavior [i.e becomes real] when their quantum particles are probabilistic.
 A: *

*Reality in the "quantum world": In quantum mechanics, the state of an isolated system, i.e. an atom or a molecule, is described by a complex vector, usually written as $\vert \psi \rangle$. This state "real" in the sense of the question and not deterministic. However, there is no way to extract full information about the state in an actual experiment. The best one can do is to test, whether the system is in some particular state, say $\vert \phi \rangle$. This could be for instance: Is the spin of the atom "up", or $\vert \uparrow \rangle$. The probability for that is $\vert \langle \uparrow \vert \psi \rangle \vert^2$ (Born rule). This is, where probability comes in. The fact, that one cannot extract all information about the state of the system by any experiment does not mean that the state is not real.



*For molecules, the concept of decoherence becomes important. Rough idea: Such a bigger system is very hard to isolate from the environment such that it will be entangled with the rest of the universe, or at least the lab, and a description in terms of pure states is not sufficient. Instead, one uses a density operator $$\rho = \sum_{n,m} p_{nm} \vert n \rangle \langle m \vert,$$ where $\lbrace \vert n \rangle \rbrace$ is an arbitrary basis of the systems Hilbert space and $\rho_{np}$ are parameters for the mixed state. Decoherence means now, that by coupling to an environment, the off-diagonal elements vanish $\rho_{nm} = p_n \delta_{nm}$ and $p_n$ are classical probabilities of the system to be in any eigenstate. If we now take any measurement, and take $\vert n \rangle$ to be the eigenstates of this measurement, the outcome will be just fixed by this classical probability that comes from not knowing the entire history of the system, but not from the intrinsic indeterminism of quantum mechanics. This is the connection to the "reality" picture in classical physics.

A: 
If in the quantum world reality is just based on observation then why atoms and molecules are real?

In classical physics our human sense of "reality" was described with mathematical formulae which extrapolated down to very small distances and times are only "real" by definition and because the formulae worked .
The need for quantum physics mathematics and formulae came because there were measurements that could not be described with the mathematics of thermodynamics, classical mechanics and classical electrodynamics, and so we have arrived at the present quantum physics which is descriptive and predictive at the level of the microcosm.
Atoms and molecules are described by quantum mechanical formulae,  which work. The problem  The problem comes with this assumption "reality is just based on observation " and "I mean, it is said that when a quantum particle is not observed it's neither spinning up nor down". The correct statement is "we cannot know how it is spinning unless we observe it".
You can say the same for classical thermodynamics and an ensemble of molecules. The formulae of thermodynamics are such that you do not know whether a molecule is going up or down, it could be doing anything for all you can know, unless you measure it( a particular molecule).

why molecules down to electrons and protons have a predictable behavior [i.e becomes real] when their quantum particles are probabilistic.

Atoms and molecules are also probabilistic in the way they interact with each other. and the formulae predicting their quantum behavior are as real as classical physics formulae, just different.
