How to file-manage an iPhone from a Windows box?
Generally speaking you can't do this on a PC (Linux or Windows) or a Mac. Though on Windows PCs you can usually get to the folder that holds music and pictures, if I remember correctly.

But really there is no way to treat an iPhone like a thumb drive without jailbreaking it or jumping through hoops that would end up (possibly) being more trouble than it is worth.

The only thing you should do is back up the phone to your PC from time to time. Yes you can use iCloud backup, which I do use, but I also change that button in iTunes and back up locally from time to time. Mostly because I am a vaguely paranoid IT guy who has seen so many people lose data because of incomplete backups that I have two backup methods for my iPhone.