Finder wants to make changes. Type your password to allow this System: 10.10.3 Any changes in Finder gives the popup window where I am asked to type my password. I can delete files so not that earlier discussed problem. Any file taken out of finder is just copying, not remove it. It started after updating to 10.10.3 and both on iMAC and Macbook Air. 

Tried everything so far....repaired my disc's permissions in reboot mode, checked terminal and compared with the empty trash problem... but nothing worked.
An solution would be much appreciated, thanks
I would recommend you updating to 10.13.2 macOS High Sierra. It should resolve the problem.