I don't use iCloud Photo Library but iCloud Photo sharing and My Photo Stream. So, I can't check my photos in the Photos on iClound.com?
Yes, only iCloud Photo Library is visible in the Photos.app at www.icloud.com, not the Shared albums and My Photo Stream.
My photos sharing between my iPhone and iPad, both in My Photo Stream and Shared albums, do not show up in the Photos.app in my iMac, is it due to the same reason?
Photos on your Mac should be showing the shared albums, if you are using the same AppleID as on your other devices. Did you enable both "my Photo Stream" and iCloud Photo Sharing in the System preferences > iCloud > Photos and in the Photos.app: Photos > Preferences > iCloud?
If yes, but the Shared albums and My Photo Stream are not shown in the "Shared" section of your Photos library, disable the shared albums and My Photo Stream again in the System Preferences, restart the Mac, then enable it again. The shared albums should slowly start to upload again. On my Mac it took a full day for the Shared albums to appear again and download the photos.