Why does uninstall → “allow program to update software" ?

I'm running Windows 8.1, and Thursday night a download/install of FileZilla (from their website) somehow led to unintentionally installing Vosteran and iSpeedPC. I didn't want these irritating programs, so...
____First, Malwarebytes found hundreds of Vosteran files, and I quarantined them. This seemed to solve that problem, although I wonder if Vosteran did any permanent damage while it was active.
____Then I tried to uninstall iSpeedPC, but after saying YES to “Are you sure...?” the next screen asked “Do you want to allow the following program to update software on this computer?” and the program was iSpeedPC, so I said NO. This question to “allow” seems unusual. Is it normal behavior for uninstalls? To uninstall on 8.1, is YES the correct answer?
____When I restarted in Safe Mode, an uninstall attempt produced an error message, “The Windows Installer Service could not be accessed. This can occur if the Windows Installer is not correctly installed."

____Two other strange things that may (or may not) be relevant are: During a Restart from Normal Mode the screen (re: functions still running) says “Task Host is stopping background tasks.” And the Microsoft Solitaire Collection no longer runs; until yesterday it was fine, but now it doesn't even have the "trying to run" icon, just its inert initial screen.
____I'm confused, don't know what is happening or how to fix it. Any help you can provide will be greatly appreciated.

Two potential solutions -- use Revo Uninstaller, or just say YES (when asked "Do you want to allow...?") -- are described in a thread in MS Forums that currently ends with my two replies.