Delete photos and videos

Warning: The Google Photos App on mobile devices uploads a copy of your device photos into Google Photos cloud storage. If one is edited or deleted in Google Photos, the same may happen to the other copy. 
See also How to delete photos from Google Photos: delete from cloud, phone, or both? - GeeksOnTour.COM  

There is no easy way to delete many photos: you will have to select them in batches of max 500 and delete. 

You can delete on many places, like the Photos tab,  albums, search results, archive, people, things, places etc, and also on the storage management tool (large files, blurry photos, unsupported videos etc)

Tip: Before deleting photos from Google Photos, you may first want to download your photos to your computer, or save them elsewhere in a safe place (not synced).  Directions for downloading methods) are here.

Delete in the Google Photos app on mobile devices

When you move items to the trash bin in the Google Photos app on mobile devices, those items will also be deleted from every device that syncs to your Google Photos library.  You should only use this when you never want to see that photo again. 

Delete in Google Photos (web app)

Deleting items in the web app https://photos.google.com will also delete from all synced devices. See below how you can avoid this. 

Delete from Google Photos but not from mobile devices

Important: the Google Photos app on mobile devices shows (i) photos that are on the device (backed up or not), and (ii) photos that are on https://photos.google.com when signed in to the same account. This often leads to confusion, thinking that a photo shown in the Google Photos app is backed up to Google Photos.
When you delete a photo in the Google Photos app on mobile devices it will also be deleted from the device (if present). You must delete from  https://photos.google.com, and not from the Google Photos app! 

Delete from https://photos.google.com 

Note: you can also delete large items via Google One storage management 

When you delete a photo from https://photos.google.com it will also be deleted from all synced devices. In practice that are only mobile devices (phones and tablets) since syncing with computers has been disabled.  

There is no official way of deleting photos from Google Photos without deleting them from your mobile device. There are however ways to avoid this:

Links:
https://www.guidingtech.com/delete-photos-google-photos/
https://www.guidingtech.com/delete-photos-google-photos-but-not-icloud/  
https://www.technobezz.com/how-to-delete-photos-from-google-photos-but-not-your-smartphone/ 

Delete device copy but keep backup

Delete from Gallery or another File manager

The cloud copy will not be deleted, but you must be sure that there is one: view your photos on a computer or web browser at  https://photos.google.com/ and sign in with the same Google account you use on your phone - you will see all of your backed up pictures there. 

Delete in the Google Photos app

Do not delete straightforward from within Google Photos: that will also delete the cloud copy.
It is safe to delete the device copy from your phone by following methods: device photos will only be deleted when there is a backup. See also Three ways to Delete Photos with Google Photos 

Recover items from trash

Deleted items stay in your trash bin for 60 days and then are permanently deleted. There is no way to recover them once they are permanently deleted.

To recover items from trash before 60 days have passed since deletion: