1) Photos taken with my iPhone, which have been synched to Photos, deleted from the camera roll, and synched back as part of an album DO NOT appear as duplicates within Moments, even though they are in My Photo Stream as well as a synched album. It only happens with photos from a non-iOS camera.
When you delete a photo from an iOS device's camera roll, it also deletes it from PhotoStream. Or deleting from PhotoStream on an iOS device will also delete it's original from the camera roll. So, there is no copy on the iOS device to be seen as a duplicate.
Read the last 2 points here: https://support.apple.com/en-us/HT201317
The reverse is also true. If you import pictures to a computer from another device such as a camera, those photos get put to PhotoStream from that computer. If you delete the photo from that same computer, it will also delete it from PhotoStream as well. One difference is, from a computer, you can actually just remove a photo from the PhotoStream album (not delete) where it remains in the Photos Library. You can't choose "remove from album" on an iPhone, but you can on a computer.
2) Albums created using iCloud Photo Sharing do not produce duplicates in Moments.
iCloud Photo Sharing are not part of any library until they are imported, and will not show up in Moments unless they are part of the Library. PhotoStream seems to be the exception to this on an iOS device.
In reality, I think PhotoStream should also not show in Moments, then you would not have the duplicate issue.
Remember, iTunes is not keeping the 2 libraries synced up. You are using iTunes to copy specific photos or albums from one device's photo library to another. It is a true separate copy from what exists on the iPhone's camera roll or PhotoStream. So apparently, devices do not check the metadata to screen for duplicates when pictures come from different sources.
So, maybe that's a feedback point to send to Apple.