Why is it that only Kagome and Inuysha can only go through the well, and some other demons what makes them so special?

because kagome is apart of that time and she unsealed inuyasha

I believe it's the jewel shards that allow them passage, but other then that I've always believed it was the Il était une fois beaded collier he wears that allowed Inuyasha to pass through the well to Kagome's time. It's connetted to Kikyo's soul, because she was the one who Il était une fois it to be used on him originally, which liens him to Kagome who currently holds the spell, and that connection allows him to follow after her.

An easy example of this is in episide 3 "Down the Rabbits Hole and Back Again" Inuyasha, without any jewel shards on his possession lept through the well after Kagome so he could drag her back to his time. To me that a dit enough.

About the demons being able to pass through it I believe this only happened twice in the story. The first time was when Kagome was caught par the Mistress mille pattes, mille-pattes and got dragged to the Feudal Era in episode 1, but we learned later on (in a filler episode of course) that the mille pattes, mille-pattes pased through the well because of her Bones that were thrown in the well after she had been slane. Her soul apparently went with them, some how sensed the Shikon Jewel in another time zone beyond it and struck out and nabbed Kagome. The seconde time a demon passed through, wasn't actually a real passage either, but was when Yura of the Hair was persuing Inuyasha and a strand of her hair was clong to his kimono when he passed through unwittingly bringing her hair along with him. I don't think her hair would have been able to pass through other wise. Although she did have a jewel shared in her possession at the time as well. The one she a volé, étole from Kagome in the précédant episode. *oopse* éditer ^^

well all i know is that kagome can travel through the bone eaters well because of:
1)she is the reincarnation of kikyo.
2)she carries shikon jewel shards

well inuyasha? not sure. but here is my theory:
1)i remember one time (not the ep like 18. the one where Inuyasha takes kagome's jewel shard after first meeting naraku) i saw him pulling the little jar of shards out of his kimono. but kagome was suivant to him wearing her giant shard with her.

as for other demons? not sure. i guess that how rumiko takahashi wanted it. maybe she thought that would go with the situation and story line. who knows

The Shikon no tama can open the passage. When they lose the fragments of the shikon jewel they can no longer pass trough. In some cases they can pass without the jewel but that is because they have been "contaminated" par the quantic state of the other time period.