[spoil]Wishing the jewel out of existence thrusts Kagome back into her own time for three years until she is finally able to re-open the gateway after she graduates school. She returns to the feudal era and becomes Inuyasha's wife. I assume she can travel back and forth between the times still because the well serves as a gateway, but the implication story wise is the feudal era becomes her new home with Inuyasha.
Neither the manga nor the anime give any real clues about what happens to demons that makes them essentially non-existent in the modern era, but I attribute that to general story themes like in LotR where the age of magic is coming to an end and the story takes place in the twilight years of more fantastical ages. I imagine it's the same in Inuyasha. Eventually the demons, for whatever reason, move away from the material realm. You could say that Nuraku actually destroyed a great number of demons in his attempt to become immortal and without the jewel, maybe demons actually begin to lose their hold on the material realm.
Just speculating obviously. I imagine though Inuyasha stays with Kagome until she dies of natural causes and either finds love later or never loves again. Depends on how feelsy you wanna be. I imagine they'll have children though.[/spoil]
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So I did more research since your post, and here is what I figured out...
1. Partially agreed, I would like to add in my own speculation is that because she guessed correctly for the Shikon jewel to disappear. The jewel granted her a real wish, but I also got the sense that the jewel wanted to survive as much as possible demeaning my hypothesis incorrect.
The part I do disagree is that the well is open, I think the bone-eater's well is only open as a predestination event to send Kagome back into the past with the jewel. Remember that when Kikyo died, she asked for the jewel to be burnt so she could take it to the underworld. Problem though is that Kagome is a reincarnation of Kikyo, who was born with the jewel in her body from what transpired in Kikyo's cremation. The jewel knew what was going to happen and summoned her into the past to wish upon it at the ending of the show.
There was actually a later chapter made by Takahashi, which takes place 6 months later. She made it with other manga artists to raise money for the tsunami and earthquake victims. It is entitled, "Since Then" and Kagome says via English translation this quote; "I decided to live with Inuyasha..and come to this world". The chapter also has a synopsis from Takahaski which says, "The girl who became an inhabitant of the Feudal World: Kagome!". It doesn't quite confirm that the well is shut or not, but based on how they're worded, I guarantee that it is. That is not to say that Kagome is permanently stuck; in Inuyasha's time, especially with demons existing, there probably is some type of time travel type of magic, even if it is meant to go back to the Netherworlds to attain it.
2. Great points, absolutely can see that happening. Not trying to over complicate the situation since I don't think Takahashi did enough thinking to overcome this problem. Just that, logically and mathematically speaking, someone like Sesshomaru should technically still be alive. Especially if you consider Seshomaru's pure blood genes and his power, IMO he's easily more powerful than Inuyasha.
3. As I said in my calculations, the absolute worst case and minimum life expectancy for Inuyasha is between 800 to 1200. 800 years old puts him at the equivalent human age of early 60s. If he lives close to 1000, which is entirely possible, he would probably be in the early-late to middle 70s. There is even a chance he might outlive some of his children as well. Since he's 50% demon and Kagome is 100% human, their offspring would then be 25% demon blood. They definitely wouldn't be making the age of 800 or 900, but perhaps middle range of 200 years old isn't out of the question.
Now in terms of Kikyo or Kagome, I thought the anime conducted the scenes as a solid conclusion at the time, but with some time to think, I believe it's lacking overall. Or maybe it's just my personality, because for me, if I loved someone as much as I did Kikyo, I don't think I could remarry. Not only that, but love someone as much as Kikyo AND Kagome, while both die when I'm still at a fairly young age. I just can't think of remarriage, that's why I always thought the relationship would be weird. Except if Inuyasha decided to use the Shikon jewel to turn human (as he planned with Kikyo).
Not only that, but losing someone extremely important as Kikyo and then a week later, almost kiss Kagome in her room. It actually tells me that he didn't have as deep of feelings for her as we all thought he did. Furthermore, it's not like Kikyo soured the relationship as she did when she came back from the dead earlier on. She realized that Nuraku was the one behind it, she actually turned more jealous over Kagome as the series went along IMO.
Sorry I tend to ramble on a bit too much on situations like this.
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