How do we know what we know about Custer's last stand? Are our sources exclusively native? Custer has a reputation as a reckless general and a political opportunist- how much of this was contemporary, vs after the fact? Should he have seen it coming? What were the battle's lasting repercussions?

This is kind of a Thanksgiving version of an answer since I am not at home, don't have access to my books and am writing purely from memory. Should it happen that I have the time and energy to more adequately address all of your questions at some later date --like maybe tomorrow?-- I will.

With regard to whether or not Custer should have seen it coming, the answer is definitively yes. Virtually all of his scouts (an assortment of Crows and Arikaras as well as some old time traders like Charley Reynolds and Mitch Bouyer) repeatedly told him --as the 7th cavalry progressed from the Yellowstone, down the Rosebud and up to the divide separating it from the Little Bighorn-- that there was sign of thousands of horses and travois having passed through the area and converging on the Little Bighorn. All of the scouts would also have been very aware that the Lakota were holding a great council, as they traditionally did every year, and would have known that they had moved it to the Little Bighorn (or "Greasy Grass" as the Indians knew it) from the Black Hills under pressure from gold-seekers and a US government policy of official indifference to their treaty rights, which is just to say that they would have had one more reason to be hostile.

The scouts would also have known that among the thousands of warriors camped along the Greasy Grass were a handful of known "hostiles" such as Crazy Horse, Gall, Sitting Bull, American Horse and Two Moons, a Cheyenne war chief who'd seen his wife and children killed by Custer's forces on the Washita in 1868. Custer would have had zero reason to expect anything less than a fight to the death from these men, and while the 7th Cavalry did contain a number of new recruits, many of its veterans would have known that they could expect no mercy from the hostiles.

According to several sources I've read, the Arikara and Crow scouts who did not flee immediately before the battle (there were a handful who wisely got the hell out of there) began singing their death songs in the predawn hours as Custer deployed his forces.

The upshot is that Custer had plenty of warning that he was walking into a deathtrap and, given his experience as an Indian fighter, certainly should have known better. As for why he did not, there are several possibilities. One is that he was relying on his past experience, as on the Washita, which told him that an early dawn attack against a sleeping Indian village could yield good results if it were conducted with speed and aplomb. Another, concomitant factor, may have been his refusal to acknowledge the actual numbers of Lakota and Northern Cheyenne camped along the Little Bighorn. While Custer certainly knew that he was taking a big chance --he had high political ambitions and felt that a great victory could propel him, ultimately, to the presidency-- it's not clear that he recognized that he was taking on 3-5k (possibly more) Lakota and Cheyenne warriors even though, had he listened to his scouts, he clearly should have.

Ultimately then, no matter how one slices it, Custer had access to plenty of good intelligence as to the disposition and numbers of the Lakota and Cheyenne camped along the Greasy Grass and definitely should have known that he had zero chance of victory.