Not a physicist either, but I will give it a shot. Relativity tells us that their is no universal time ordering of arbitrary events, you can find reference frames where A occurs before B and where B occurs before A if the events occur at different positions in space. There is nonetheless still a global causal ordering of events - events can only be influenced by events in their past light cone and they can only influence events in their future light cone and light cones do not change when you switch reference frames so everybody agrees on this causal ordering.
I also think your view of quantum effects has some misconceptions. A photon is what it is, it does not switch between particle like and wave like behavior. It goes neither through one slit, nor through the other, nor through both or neither. It is really different from a classical wave or a classical particle. But that is just the way the universe works, the strange thing is not what the photon does, but that macroscopic objects do not behave like quantum objects.
I am not so sure about that one, but I think there are not so many people believing that the wave function collapse is a real fundamental thing. It is just incompatible with the unitary evolution of the wave function and causes you all the trouble figuring out what constitutes a measurement and what not. This is obviously an open problem but the collapse postulate is probably viewed as an approximation at best by most.
And the problem of the arrow of time kind of sits on top of the problem what time is in the first place. One view I picked up recently makes a lot of sense to me but I did not have much time yet to really look at it in some depth. Anyway, here we go. Fundamentally all fundamental particles are massless and travel at the speed of light. This kind of removes the need for time, massless particles travelling at the speed of light experience no time and if everything just moves at the speed of light there is no real need to use time to describe velocities, changes of position over time, because it is implied due to everything moving at the speed of light.
But then fundamental particles interact with each other, they attract and repel one and another. This opens the possibility that the composite system of several fundamental particles moves at a speed slower than the speed of light while all the constituents still just move at the speed of light. It are only the composite systems that are not following lightlike trajectories which experience time. One just compares the rate at which processes occur in composite systems to establish a time base.
Take a photon clock, a photon bouncing back and forth between two mirrors a fixed distance apart. All the electrons, quarks and gluons in the mirrors travel at the speed of light but the composite system is at rest from your point of view. The events of the photon hitting one mirror and then the other establish a time base for you. If you then boost the photon clock away from you with a very high speed, maybe close to the speed of light, the photon takes longer to bounce back and forth between the mirrors because it moves still at the speed of light but the mirror kind of runs away from the photon, that is time dilation. And if you boost another person along with the mirror and look at the cells of that person you see the same thing, molecules take longer to move around and reach their destination because all the parts of the cell move with a high speed and velocities do not simply add linearly, the person ages slower.
As said, I had not yet the opportunity to really look into this way of thinking. Especially I am not sure if really all mass stems from dynamic processes or if there are some fundamentally massive things out there. Maybe someone can provide some further insides whether this is a valid or helpful way of thinking about it.