When I unistall an application I want to check for all remaining files on computer. Searching them with Finder doesn't show any protected file, for instance from Library, and also hidden files are never included in search. Can this be controlled or changed?
You can add the System files and File visibility attributes to the filter bar:
Files that start with a period are still excluded though.
This makes Finder show hidden files:
mdfind includes system files by default, but it doesn't include hidden files unless you specify kMDItemFSInvisible=1.