Beepster : To answer your questions :
* No, and this using web downloads direct from the purchasing site(s)
* Yes, happens also with most any anti-virus at one time or another
* Yes, as long as you downloaded from a reputable source.
I only use the Registry part of Ccleaner, I set my web browser to erase temporary files after 3 days and limit the size of the cache to 250 MB. My personal preferences.
Once a month, I run Ccleaner alongside Malwarebytes and a quick scan of MSE. That catches 99.99% of things.
FYI, Ccleaner is the most downloaded software in France, according to OneNet. So I think its very safe to use, but then you'll always have sceptics.
So don't worry about the false positives long as you downloaded from a reputable source.
Cheers,
Jerry