Photos backed up to iCloud and then deleted from phone were deleted from iCloud

I had photos on my iPhone 5S that I had automatically backed up to iCloud photos. I checked that they were there. From what I understood, if I backed up photos and videos to iCloud, they would stay there even if I deleted them from my iPhone. However, once I deleted these photos from my iPhone, they were gone from iCloud as well.

1) Am I doing something wrong?

2) Can those photos be recovered?

3) If this is the way iCloud works (deleting photos that are deleted on other devices as well), is there another good app to use to automatically back up and STORE all of my iPhone photos?