>can the unknown that's being collapsed not be a pre-determined value that therefore is not traveling faster than the speed of light?

This is known as a "hidden variable theory". People will tell you that a local (things can only affect their immediate surroundings) version of the theory is impossible because it would be a violation of Bell's inequality, but there is a loophole that requires accepting the idea of "superdeterminism". This is the idea that where what measurement a scientist chooses to measure is predetermined and correlated with what the particle being measured is going to do.

So if a particle lands on a screen according to distribution p when going through a double slit, but with distribution p' when one of the slits is measured at, conventional QM says that the measurement "collapses the wave function". But a superdeterministic local hidden variable theory would imply that the choice of whether to measure at the slit or not was already set in stone at the same time that the particle "decided" which path to take to land on the screen, more or less.

If you split up an entangled pair of particles and measure them in a the same 50/50 basis simultaneously (sort of like a coin flip) at distantly removed places, the results will be individually random but perfectly correlated when compared with each other. It seems natural to assume that something here was pre-determined. i.e. There's was some kind of hidden information that we haven't found a way to measure yet. The way in which the coin-tosses were going to pan out was determined when the pair of particles were entangled.

Quantum physics makes predictions that suggest this isn't so. You can design experiments (e.g. A Bell inequality test) in which quantum physics predicts correlations that go beyond what would be possible with some hidden local information attached to the entangled particles that we just don't know about. Experiments don't prove theories to be correct. That's not how science works. However, experimental tests of Bell inequalities have pretty conclusively shown that local hidden variable theories are inadequate to explain what's going on.

Yes, it appears what Einstein called "spooky action at a distance" seems to propagate close to instantly. It's important to appreciate that you can't transmit information this way though. We can only make sense of the quantum correlations after communicating other information at classical speeds. Sometimes you see quantum entanglement devices allowing FTL communication in sci-fi, but that's pure horse hockey.

That all being said, I don't understand quantum physics either.

One of the "coping mechanisms" is to say that information cannot travel faster than light, even if entanglement is propagated instantaneously and measurement acts faster than light. If Alice and Bob share an entangled pair of spins and Alice measures it, Bob has gained no information until Alice communicates (sublight speed) her result. No new information is shared at measurement time. This is known as the no-communication theorem.