Dear Mark,
Its really hard to diagnose what the root-cause of the problems you mention with the little amount of information you provided. What OS are you running on?(version, architecture etc) What version of Installer are you using?
You mentioned an upgrading of 5.6 to 5.7, Did you verified there are no conflicting features between these versions?
https://dev.mysql.com/doc/refman/5.7/en/upgrading-from-previous-series.html
http://dev.mysql.com/doc/refman/5.7/en/upgrading.html
For all the examples you posted, I will assume you're working with the latest version of our web installer downloaded from here:
http://dev.mysql.com/downloads/installer/
The defaults are expected to work in the 99% of the cases. That said...
For example A, How is it preventing you from installing 5.7 back?
Is 5.7 server grayed out in the Custom Install (the one that says 'Select Products and Features') screen? Probably the service was still running until next restart. Follow screen instructions carefully to ensure a complete removal before attempting any re-install. Plus, uninstall the server is not always required. You can usually click Reconfigure on the Installer dashboard.
For Example B, there are several reasons why this could be happening. Many of them not even related to the server's MSI or the Installer, but just to name a few of these: Corrupted my.ini file, Incorrect windows service configuration (path, credentials, installed binaries in path with not accessible because lacking permissions with current account...)
All mentioned above are usually caused by users when they customize their environments without using the official tools, for this case Installer.
From what I could gathered on your findings, seems like you accidentally deleted these folders and caused MySQL service to be broken. Please take into account that deleting folders and files inside Windows folders like %programdata% could end up causing more than one program to be broken in the end, not only MySQL's.
For Example C, seems part of the same problem. You may have accidentally deleted a Workbench folder used to store the connections.
As for the latest problem you reported, the stack trace you pasted reveals the MSI for the server 5.7.16 was still downloading when you attempted to run it. I presume you you were attempting to do so from within explorer.exe or other file browser without allowing the download to finish in the installer first, (which is not recommended).