I want to understand and track that the executable program / application / process is running on my computer. How can I find all the files (for example, ouput files, log files, etc.) that he opened or accesses when he is running?
Process Explorer has a second panel displaying all open descriptors:
Also, Process Monitor can monitor and register all access to the registry and file from the process.
Process Monitor sounds exactly what you are looking for.
Just find your process and it will tell you in detail what this process is doing, not Process Explorer.