Fio reincarnated into a physical body. She marks the first human to reincarnate after the end of humanity from the events of NieR Replicant. In that sense, His wish came true; a miracle happened and humanity has hope for revival.

It is left unclear. What is likely the case is that it is similar to Kainé making a miracle happen to bring back the World-Ender during Ending E / The Lost World.

My interpretation is that it was not possible before in prior games, but is now, and that Fio was able to reincarnate because it was the combined power of Her (who has the power of both the Red Girl / N2 and power of Sleeping Beauty Quantum Server, and Sleeping Beauty is confirmed to be powered by a massive amount of maso) as well as the human data of the Quantum Server of the Moon (which required time to evolve enough to see other branches and potentially Accord providing weapons that it could extract the stories of). 

Essentially, this interpretation is that the reincarnation was possible because of the work of the original humans, maso from Angelus, power from the machine lifeforms (and by proxy aliens), and power from androids all combining together into one miracle, and only with all that is it able to happen.

It is left open-ended. Reincarnation is the goal Mama has, and Fio has proven it to be possible, so there is a chance that they will reincarnate in the future. For now, they remain in The Cage and in their own worlds and records, but with new memories and a chance to forge a happier future than what they had in their original worlds.

That book is the same book that Accord carries around with her in Drakengard 3.

Nobody important; they show that She has unfrozen time, so all of the machine lifeforms and androids can live once more. In that sense, the world now has machine lifeforms, androids, and one human within it.

It is not made clear. It is thought to possibly be powering down / deactivating all mechanical life on Earth, but that is speculation as we do not have a definitive answer.

This is something not directly mentioned in the game, but a term from Drakengard 3. It is the "utter collapse of the world." Its relevance to this game are that it's common theorized that Her freezing time could be the Falldown, or a timeline where humans have no chance of surviving causes the Falldown, where a branch will then be sealed and moved onto another to try and find one where humans do survive. In that sense, the theory is that this ending means that the Falldown has either been worked past with unfreezing time or outright prevented and no longer a thread since Fio is proof that humanity can revive. 

But again, this is speculation at the moment. Nothing is outright confirmed, it just is a common point of discussion as a result.

The branch of the novelization of Drakengard 3 led to Drakengard. Ending E of Drakengard led to NieR Gestalt/RepliCant. Ending D of NieR Gestalt/RepliCant led to The Lost World novella, which then led to NieR: Automata. Ending E of NieR: Automata happens and then eventually, time loops back around and eventually He creates Her. Then, NieR Replicant ver.1.22... happens with Ending E, which leads to an alternate set of events since He is deceased, and eventually leading to further time loops with Her all alone. She later merges with the Red Girl, and in each branch, tries to attack and destroy The Cage (and is successful as seen in Record: The Cage of Rebirth). After 62,472 cycles, NieR Re[in]carnation happens as that final branch where by miracle the Singularity known as Levania chooses to save Fio, and Fio thus goes on to save Her and bring hope for the future.

It is not confirmed, but it is likely between NieR Replicant ver.1.22... and NieR Re[in]carnation due to easter eggs referencing this game in the anime.

The Cursed God presumably acted as something meant to attack The Cage when at its weakest point as an ultimate weapon, so once ready, it revealed its true form. Mourning Mother and the babies are likely chosen to resemble the Watchers and the Queen Beast to have a digital recreation of what doomed humanity to be what snuffs out the final bastion of humanity. This is the assumption, as other details are unclear.

In her hidden stories, 10H was left behind to fight the babies following Chapter 23 with her sacrifice. She ends up making a small area and writing stories and eventually making a friend, who she tells those stories to. Friend eventually ends up choosing her own will to depart and see the world, so 10H gives Friend a matching form and all of 10H's memories, while 10H stays behind to keep the mini-Cage intact so that Friend can even exist, and Friend manages to escape and reach Mama. Friend isn't 10H, but she can be interpreted as a separate entity, copy, reincarnation, etc. of 10H that is able to have a happy ending. It is implied by 10H's fourth hidden story ending that the original 10H data is still within The Cage and is still waiting for somebody to help her, but as Friend did find Mama and wanted to save 10H, there is still a possibility that the original 10H is rescued one day.

Yes. They are an endless amount of branches and possible outcomes of the world, and each story in the game is what really did happen in those branches. The Cage acts as both simulating those branches and being records of them. For example, this would mean that while the original Fio of her branch died from starvation in the ruins, a copy of her data in The Cage ended up being who we watch over who ends up being the one to reincarnate. Another example would be that in the branch the game takes place in, Yuzuki and Hina both die during the wars on the Legion, but the ones in The Cage come from a branch where the Queen Beast never attacked. Both events did happen, but in different branches.

Some are different points in time, but many are also separate branches recorded by The Cage. This is also proven by Zero's Divergent Sister description, which talks about hoping that the branch Zero is in where she can have a happy branch with her sisters never ends (despite the threat of the Flower).

It at least takes place sometime after the events of this branch's version of NieR: Automata (as described in that timeline earlier), but it may possibly take place in March 12024 (as that is the date in Gayle's 5th hidden story, being 10,000 years after the real month that the final chapter of NieR Re[in]carnation released. It is not confirmed or stated anywhere else if that is the correct time or not.

The developers have confirmed in livestream that it was meant to be misdirection created by the corruption of information as a result of Her attacks.

All four were sent to help Her reach Her goals. Carrier disrupts stories in The Cage, and the others united the Sun and Moon as representations of opening a port in the moon server that could be used as a direct attack on The Cage from the Earth.

A livestream confirmed that Carrier at least does have a real Pod form (which could be a possible reason that Mama trusted Carrier) and that Carrier was corrupted by Her, though it is unclear if the same applies to Dark Mama / Babe / Papa.

It was likely thought of and planned out with both NieR Replicant ver.1.22... and NieR: Automata ver.1.1a in mind. According to interviews, the anime was in pre-production before the announcement of the remaster as well as NieR Re[in]carnation. The remaster's Ending E and the novella The Lost World Appendix ver.1.22... both focus on Him and Her, with the novella also outlining His final thoughts before dying, talking about creating Her, and describing Him seeing structures that sound similar to The Cage. It is likely that based on this, the plot of this game was planned ahead of the remaster and anime.

There were plans and ideas written up which were talked about by some of the people who worked on the game on Twitter. It is possible that they will appear in the book releasing in November (as long as other possible clarification of unclear stuff).

Presumably yes for the ones related to other Yoko Taro works due to being records of separate branches and/or the past. It is not clear if the collabs with other games like Persona 5 are canon.

We wait for the book for additional information (as it has additional stories that will release in it). There's also the Extra Content button at the top of the site, which will include any content not covered in this site. Aside from that... you've finished NieR Re[in]carnation.