Not always, there are some installers that do handle the uninstallation of folders, files and icons at the time of uninstallation, but they can be left over in folders such as Program Data, in the registry or even in the original installation folder.

I recommend you use Revo Uninstaller, this program is responsible for uninstalling any program and remove it completely from your computer.

Not necessarily, some leave behind files such as settings and data. They may also leave changes to the registry, for example, to stop you from reinstalling trial versions of programs.

Not exactly, when uninstalling a program there are usually some junk files such as temporary or configuration files that as system extensions are not deleted as a precaution in case they are still used by the operating system, in case you know they will not be used by any other program you can delete them manually, you should also check all subfolders with which the program interacted to see if there is no temporary or residue.