I accidentally deleted all of my photos thinking they would remain in the iCloud. Can I retrieve them? If not, how can I retrieve from an extrernal hard drive?

After 30 days the photos are automatically erased from iCloud server so can't be recovered , if you had transferred photos to an external hard drive connect the Mac to it see the article https://support.apple.com/en-in/guide/mac-help/mchl027f1d66/mac

And then import photos https://support.apple.com/guide/photos/from-storage-devices-dvds-and-more-phtae4e05c67/mac

How have you been using iCloud Photos? Is "Optimise Mac Storage" enabled? Then many of your photos may only have been in iCloud and not stored on your Mac in a full resolution and your Time Machine backups will not have included all your photos in full resolution, only optimised versions. Then you cannot recover the photos from a Time Machine backup. But if you not have used Optimise Mac Storage, try to restore the Photos Library from Time Machine, if you made regular backups.

How can I retrieve all my photos deleted over 30 days ago?

You can't.

If so, can I retrieve them from my external hard drive?

Did you copy them there?