What happens to shared photos when i delete them locally?
Removing photos from your Camera Roll will not remove them from Shared Albums. It will, however, remove them from iCloud Photo Library, both in iCloud itself and all of your devices.

If you have iCloud Photo Library turned on and the Optimize Phone Storage setting enabled, there's no way to further reduce the amount of storage taken by photos in your camera roll other than simply deleting them (again, subject to the caveat in the first paragraph).

Deleting photos using Photos.app should not affect their storage in the Google Photos cloud. (Deleting them with Google Photos will cause them to be removed from the Google Photos cloud.)