Are favorites in the Photos app suppose to sync between devices?
They will (or should) sync between devices if you are using iCloud Photo Library, otherwise, e.g. when syncing just the PhotoStream, favourites do not sync.

I just tested this on a device running iOS 12.1.3 and macOS Mojave 10.14.3 by favoriting a photo in the iOS photos app, and not only did the photo appear in the Favorites album in Photos.app on Mac, the Favorites album was automatically created in both places. (I don't use Favorites, but they do seem to work for me.)

According to Apple's Support article for iCloud Photo Library, edits do indeed sync between devices. I also confirmed this just now by cropping a photo on my Mac, and watching the cropped photo appear on my iOS device.

NB: if you are trying to sync favorites between devices using a hardline sync such as iTunes, I am unable to describe what the correct behavior for that is, as I don't have a setup to test it with currently, nor could I find any information on Apple's support website.