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.)

As tubedogg pointed out, the photos removed from Icloud Photo Library will still be available from the shared albums (because they are copies) BUT be aware that shared copies are scaled down to a resolution of 2048px on the long edge (5400 px for panoramic photos).

So if you share a 20 megapixel photo via Icloud Photo Sharing, the shared photo will be something like 3,5 MP (generally, not related to the deletion).

See https://support.apple.com/en-us/HT202786 for more on these limitations.