Couple questions: 1. Where is the permit for the checkpoint?

The permit for the checkpoint is in sakata village. When you first get there you will not be able to buy it. You must first defeat Sara in Yamasuchi (sp?) village. Then you can go back to Sakata to get the permit. Once in town go south then east until you come to the last open building on that end of town (its on a corner). The man will be there now to sell the permit. Remember you will have to defeat Sara twice. Once in Yamasuchi village and once in her lair before you can get it. You will not meet Datara until the end of the game as he is extremely difficult to beat (he is in Tempest tower). New Moon Cave is a side quest. You can defeat Sara there later if you wish to level up. Sesshomaru will help you beat her. You do not have to talk to the sea god if you do not wish to. As for after the midterms I believe the next step is going to the park and finding Monk Sen (this is actually Tsugumi in disguise :spoiler You will need to eventually find 5 sutras and defeat the main demon in the park. Save before you enter because you will not be able to leave the park once you enter to talk to Monk Sen. I do not remember the pathways specifically. However go to the gamespot.com forums on this game. Krazykitty has posted a mini walkthrough to the game. She/he has beaten the game and will answer any further questions. (I don't remember past here where to go and when). Good luck. She has helped me and was the one who told me what I just told you about getting the permit.

1\2\3) after you beat sara and go do the mid terms you have to go to the park and there you will see someone running saying monster and then go to the bottom left of the screen, after a little walking inuyasha will say that he senses a demonic aura (i think) and then you must find monk sen's shrine, you have to find 5 wooden things with seals on them, take the seals off, then find the main monster after that you go back to kaede, then you have to find hachi, he is on the other side of the check point, to get through the checkpoint you have to go to the castle (if you see the path that goes from the checkpoint, follow that) then talk to alot of people and someone will say that they are inocent and they know what really happened that you didn't kill a human but a demon, anyway, after that you find hachi somewhere in that same area, then you have to go somewhere to the east/right to a town that is in between a mountain and a river, after that go find hachi again, and he will take you to this one place, from there you go to a town where almost no one is there, then someone will say that demons have taken the young villagers, then you have to go to the fort where they are, none of the demons will attack you, so find the villagers which are in the place to the right of where you talked with the main demon, they will go back to there village without you, then where you talked with the main demon, you have to go back to that spot, go up where he was standing and walk in that cave, go through there and you will exit the cave, then go (i think) kindof to the left, then up, then right, untill you find dataka's shrine, it's somewhere around there, monk sen will tell you that you have to find the two gaurdians of dataka, and you have to find the two keys, that's as far as I am, so yea, it's long, but I hoped it helped :D
4) the thing to talk to the god in new moon cave? Huh, I don't understand the question, sorry, I havn't been to the new moon cave, so I have no idea, again sorry but I hope I helped anyway :D with the other questions that is :D

The permit is in a castle behind the checkpoint(forgot the name) anyways you have to go inside the place and you have to buy it from a inside a house/store.