Hi, Let's see if I can answer some of that.
Nags:
They are what they are and all freeware contains them.
Once you have seen each of the nags it shouldn't show you it again for a while (but may show a different new offer if there is one).
However some people clear out CCleaners own cookies, (either by changing settings in CCleaner itself or using another cleaner), and if/when they do that CCleaner doesn't know that it has already shown the nag so will show it again.
Of course buying a Pro licence will stop most of it.
You'll still get reminders and cut price offers when your licence is due for renewal.
CCleaner doing things on it's own, running at startup:
A few settings can do that in CCleaner Free. (more in Pro).
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If you have Options>Settings>"Run a one time clean with the Custom Clean tool when you start Windows" ticked then it will do just that.
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Options>Smart Cleaning if enabled will run in the background and ocassionaly clear built up junk. It will put a CCleaner icon in your system tray.
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Options>Updates>"Keep CCleaner updated automatically" if ticked also runs in the background, and will put the icon in the tray.
None of those should open the CCleaner window though, they run in the background.
I'm not sure what the defaults are in the Free version these days, but think that both Smart Cleaning and Automatic updates are on by default - You can turn them off if you don't want that.
As you say an automatic check for updates might fetch back a 'limited time/low price' offer to upgrade to pro. (Not sure but I could easily see it doing that).
Controlled Folder Access:
CFA is off by default in Windows, you have to turn it on yourself.
I turned CFA on a long time ago when it first came out; and quickly turned it off again because it was always causing problems, throwing up false positives and stopping non-Microsoft apps from working properly.
CFA is a bit of a nanny who likes to keep you 'safe' by never allowing you to do anything that a grown-up might do.
It will often block cleaners, Antivirus apps, and other grown-up, serious, software from accessing folders that it doesn't think a 'dummy' user should access.
(MS don't think much of their customers intelligence, or of any app not written by MS).
It's even been know to stop Microsoft's own software, and sometimes the Windows operating system, from accessing folders that they need to.
Microsoft themselves say:
https://support.microsoft.com/en-us/windows/allow-an-app-to-access-controlled-folders-b5b6627a-b008-2ca2-7931-7e51e912b034
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Occasionally, an app that is safe to use will be identified as harmful. This happens because Microsoft wants to keep you safe and will sometimes err on the side of caution; however, this might interfere with how you normally use your PC. You can add an app to the list of safe or allowed apps to prevent them from being blocked.
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For 'Ocassionally' substitute 'Often' (In my experience anyway).
If you google- "\device\harddisk0\DRO folder" you'll find just some of the issues that turning on CFA can cause with that folder and others.
Of course it's your choice whether you want to keep CFA enabled or not.
If you want to keep CFA on but still let CCleaner do it's cleaning unhindered then you can make CCleaner an exception in CFA by adding it to the safe list, see that link above.