If multiple cards are put into the library this way (such as when the spell targets a melded permanent), that permanent's owner puts all the cards on top or all the cards on the bottom. They put them in whatever order they wish, and do not need to reveal the order.

The card's owner chooses whether to put it on the top or bottom of their library.

Endless Detour doesn't counter spells. A spell that can't be countered can still be put on the top or bottom of its owner's library this way.

If Endless Detour targets a token, that token is put into the library, then ceases to exist.