If I understood the wikipedia article correctly, quantum entanglement claims that information travels instantly between entangled particles. An act of measurement on one of the entangled particles changes (I think just determines) properties of other particle.
How was it proven that the properties are not just predetermined?
For example, if I have 2 particles and know its charge is zero, then if I measure one particle and its charge is positive, I know that the other particle is negative cause of law (equation), their charge was always such, even before my measurement, it was predetermined. Or math equation $x+2=4$, I know the outcome, I know operation, I know one operand, I can solve it and find $x$. I can determine $x$ but I don't change it.
Can multiple particles be entangled? What happens then?
Does the measurement of one particle effect other particles all together? If we make a math analogy with $x+y-2=0$, we measure $x$ and it is $1$, we know $y$ is $1$, but what if the equation is complex and there are multiple possible answers?
Can we say that in an atom, the nucleus and electrons is quantum entanglement?
Suppose electrons around atom nucleus not particles but just a function, and they are not determined until we measure the nucleus. For example we found +6 protons in the nucleus, now using math equation $x+6=0$, we know that there must be 6 electrons. Then we measure one electron position, and again we can determine other electron positions using some math equations. How it is different from quantum entanglement? Why we say that in this scenario everything is predetermine and we only discover it, and in another scenario some "spooky action" takes place?
How is it different from "wavefunction collapse" (measurement problem) and the "which way" double split experiment?
To me it looks like very close things.