Do I need to keep copies in Pictures if they are also in the new Photos app and in iCloud?

No, you do not need the copies in Pictures, unless you changed the Photos > Preferences > General.

By default they are set to import the photos as managed: "Importing: Copy items to the Photos Library" should be enabled. Them all photos will be stored inside your Photos library.

If you disabled this option, you will see tiny arrow badges on the thumbnails of the photos, indicating that the library is referencing them outside, if you enable the badge overlays in "View > Metadata > Referenced files".

except I notice there is a Photos Library folder in there. Do I delete this too?

NO!

The Photos Library package is the library where Photos is managing the imported photos. Don't delete or modify it. This is the item you need to backup to be able to restore your photos if something should happens to your Mac.