What happens after OS X Internet Recovery without erasing disk I want to reinstall OS X Yosemite in my MacBook Pro 2015 without erasing the disk. What will I need to reinstall after the process is done? What files are not removed from my hard drive? What files ARE removed from disk?
Almost nothing is actually removed. What happens is the installer downloads a fresh and complete set of system files - basically the things that came with the Mac out of the factory minus some iLife apps like Garageband for instance.

The installer doesn't delete any user settings, user files and doesn't even delete apps you installed.

The process is designed to make the system work whether or not you have large or small changes to the system.