Is there any way to determine when (day and time) the ccleaner was run previously? Is there a log of some sort to tell when it has been run on the computer?
Welcome to the Forum, whook.
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And about the log part, no idea. I'm sure there is.
Try the date modified time on ccleaner.exe in prefetch folder. That seems to update when cc is launched.
Alternatively (and probably easier) I've found that is you set the Last Accessed Date to be shown in your folder view, and then open program files/ccleaner, that should show the last launched/accessed date alongside ccleaner.exe. Using Properties to show the last accessed date just shows the current time, as running Properties seems to be counted as an access.