And in all the experiments all these in-between steps are considered to be "magically perfect". Nobody pays them any more attention except to mention that they're there. All mirrors reflect all photons perfectly. Polarization filters just "know" which photons to pass through and which not, etc.
This is true for simple textbook examples to teach undergraduates the fundamentals, but a realistic model of an experiment takes into account sources of noise from the imperfections of the apparatus.
But that's not how it works in real life, is it? All these parts are big, macroscopic chunks of matter with many, many atoms in them. A particle doesn't just seamlessly pass through/reflect - it bounces around in there, gets absorbed and re-emitted, and entangled with god only knows how many other particles on the way.
Yes, this is true. This is handled with the theory of "open quantum systems".
In the case of modelling discrete elements such as mirrors, etc., usually it suffices to go beyond unitary transformations acting on pure states, and generalise to Kraus operators acting on density matrices.
In general, if we're dealing with continual sources of noise, interactions with the heat bath causing the noise usually happen over such a short time scale that you can model it as instantaneous and memoryless, in which case you get Lindblad master equations and related/equivalent methods such as quantum trajectory theory. In the case when these approximations don't hold, this requires more explicit modelling of the particle/heat bath interaction and is usually a matter of active research.
A good general reference is Quantum Noise by Gardiner and Zoller, as well as Gardiner and Collet's original paper on quantum input/output relations.
The final particle that arrives at the detector at the end is almost certainly not the same particle that was emitted. And even if it by some miracle is, its quantum state is now hopelessly altered by all the obstacles it met on the way.
Fundamental quantum particles are indistinguishable. The effect on particles with distinguishable internal states such as atoms can simply be modelled by the previously mentioned Lindblad equations or Kraus operators causing transitions between internal states. The possibility of particle loss is handled by using a second quantised description.
Yet nobody seems to care about this and just assumes that it's the same particle and tries to measure it and draw conclusions from that.
I wouldn't say nobody cares. Pretty much every experimentalist these days takes the effects of noise into account.
