Apparently, the manga has three more series which are Mirai Nikki Mosaic, Mirai Nikki Paradox, and Mirai Nikki Redial. How does those three relate to the main series?
The three series are spin-offs to the main series. All of them are assumed to be canon.
Mirai Nikki: Paradox follows Aru Akise as the main character along with murmur, and takes place in an alternative timeline to the main series.
Future Diary: Mosaic features Minene Uryu (the 9th Diary Holder) as the main character and includes five chapters, each of them focusing on several arcs of the story under Minene's point of view. Some plot points are revealed that were not disclosed in the main story.
Future Diary: Redial is different from the first two as it is the only one that was animated (as an OVA). Redial covers the events in the Third World leading up to—and then slightly past—the final scene of the series. It follows the Yuno of the Third World.