For the most part I belive your question has been answered well in the comments above. One reason for limited availability of details, is that they keep changing, and no matter how much you think you are writing code for one specific version of MATLAB the reality is that large amounts of code get run over many years on many versions of MATLAB. Writing code that is easier for a human to understand frequently also makes it easier for the computer (or jit) to understand, if not now then it will in the future. If the jit/compiler can understand your code better then it can optimize it better. Most of the suggestions here: techniques for improving performance are made because following them makes the code work better with the jit. Before R2015b MATLAB could only run some code with a limited jit. In R2015b and later a completely rewritten jit (we call it an execution engine) was introduced that had very different characteristics from the previous jit. Many micro-optimizations that worked well no longer applied and much problematic code was no longer problematic. Since then we have continued to add more optimization to all areas of MATLAB code.
I will answer one specific question: Any speedup you see between two executions of MATLAB is entirely due to operating system caching of files accessed from disk. Think of restarting MATLAB as the strongest possible form of clearing.
For the most part the causes of code recompilation are farly obvious and most recompiliation takes place on an only as needed bases when the code runs. If the code file or type of the data changes, or possible functions to be called (cd or path change) or the file is explictetly cleared then code must be recompiled. Function code compiles a bit better because MATLAB knows all variables in the workspace when it is compiled instead of having to check when running.
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