On mac, are all photos in the Library? If so, do they stay there if I delete the same image in another photos folder?

Photos are only saved in the Photos Library, if you copy them into the Photos Library when you import them. This is controlled by the Photos > Settings > General: Importing. The checkmark "Copy items into the Library" should have been enabled, when you imported your Photos.

If this option has been active on import, you can delete the photos from folders in the Finder , and they will remain in Photos.

You can check, if there are photos in Photos that have not been copied into Photos with a smart album.

• File > New smart album
• Set the rule to "Photo is referenced"

Probably, but you need to be sure:

Are you running a Managed or a Referenced Library?

A Managed Library, is the default setting, and Photos copies files into the Photos  Library when Importing. The files are then stored within the Library package. In this scenario it is safe to delete files stored elsewhere.

A Referenced Library is when Photos is NOT copying the files into the Photos Library when importing because you made a change at Photo -> Preferences -> General. (You unchecked the option to copy files into the Library on import) The files are then stored where ever you put them and not in the Library package. In this scenario you are responsible for the File Management.