Deleting pictures

You can only do that if iCloud photo library is turned off on the iPad.

as long as sync is active any photo you delete off iPad will be deleted on iCloud

If you need space on the iPad you can use Optimize [device] Storage.

From:

Set up and use iCloud Photos - Apple Support

Save space on your device

iCloud Photos keeps all your photos and videos in their original, high-resolution version. You can save space on your device when you turn on Optimize Storage.

On your iPhone, iPad, or iPod touch:

1. Go to Settings > [your name] > iCloud.
2. Tap Photos.
3. Choose Optimize [device] Storage.
4. 

On your Mac:

1. Open the Photos app and click Photos in the menu bar.
2. Click Preferences.
3. Go to the iCloud tab and choose a storage setting.

If you turn on Optimize Storage, iCloud Photos automatically manages the size of your library on your device. Your original photos and videos are stored in iCloud and space-saving versions are kept on your device. Your library is optimized only when you need space, starting with the photos and videos you access least. You can download the original photos and videos over Wi-Fi or cellular when you need them. You can use Optimize Storage on your iPhone, iPad, iPod touch, and Mac.

If you turn on Download Originals, iCloud Photos keeps your original, full-resolution photos and videos in iCloud and on your device.

If you are using Photos in iCloud, it is not possible to delete the local copy of a Photo or video from a device without also deleting the iCloud copy of the file.

Photos in iCloud is principally a device synchronisation service that keeps a copy of all Photos and Videos in iCloud storage. The iCloud copy acts a backup in case of device loss or failure - and makes your photos available for viewing or download by other computers via a web browser or client App (such as iCloud for Windows).

Keep your photos safely stored and up to date on all of your devices - Apple Support

Photos in iCloud is not intended to be an independent storage archive. If you wish to keep an external archive of your photos/videos, you’ll need to use a different Cloud storage service (e.g., Google Drive, Microsoft OneDrive etc.), or an external storage device.