Can I delete pictures on my iPhone but keep them on my Mac and in the Cloud?

We are not Apple-- we are Apple users like you.

If you turn off iCloud on your phone, Settings>Photos>iCloud, then changes in Photos on your phone won't be synced with your Mac and iCloud. You could delete the pictures from your phone and no change would occur in the Photos Libraries on the Mac or on iCloud. If I were you, I would try it with a few pictures first, to make sure I had the settings right.

Are you using the option "Optimize iPhone Storage" on your phone? This causes the phone to only load small images from iCloud for viewing on the small screen. If you need the full sized images for editing or printing or zooming, then it will load those temporarily. This will save bunches of memory, and you still get to look at the pictures on the phone. This is by far the best option for someone who is already using iCloud Photos.

Do you use "Optimize Storage" on your Mac? I don't do that, because I want to keep a backup of the full sized images on an external drive. And I would want a good backup of my pictures before doing anything massive like deleting pictures! Keep in mind that iCloud is not a backup service-- it's great if a car runs over your iPad (happened to me,) but it doesn't keep copies if you delete them off your phone when the phone is connected to iCloud.

My iPad was only weeks old, and I had AppleCare which replaced it.

Having "Optimize Storage" checked on your phone means that some pictures are there only in the smaller, lower resolution form. So, in that case, if you disconnect from iCloud, it is suggesting that you might want to first download the full sized files before you disconnect. Apparently your other option is to wipe all the pictures off.

Are you sure you need more storage? I ask because the picture storage is flexible-- it keeps the full images until you need more space. So you phone may appear more full than it really is.