A
variety of maps and star charts were made by indigenous American cultures.
Honestly, I'd just recommend you read Guns Germs and Steel, and don't worry about all the grief it gets. It does an excellent job as an introductory to questions like yours, and while it doesn't have everything right it's incredibly easy to look up where Diamond got things wrong.
But if we're getting into domesticates, I have a fascination with moose domestication, in which case if it occurred in North America, I could imagine the settled peoples of the Plains using them like war elephants in battles as well as in peace (plowing), thanks to their potential. But that's a far off hope from OTL history, the most likely domesticate would be caribou which probably wouldn't amount to much outside the northern regions/Rocky Mountains. You won't be able to replicate the horse culture of the Great Plains with caribou, sadly.
Can't really be feasibly done. Moose are finicky eaters that are hard to get their diet right, they can be kept in some small groups, but they're still solitary and need to be let alone to forage for long periods of time. They also don't like to be kept in stalls, though that might not be an issue in some circumstances. You can still tame them and potentially make domesticates out of them, but it'd be far from straightforward. If they were domesticated they'd fill more of a 'water buffalo' position than that of a horse; they take more to swamps and shallow water than the open plains -- though they can run pretty fast they're not exactly as cursorial as a horse, either.
Don't sell yourself too short on reindeer; they may not be able to fulfill a Great Plains horse culture...but you have most of Canada and some parts of the United States to work with, too! There's lots of stuff you can do with that and horses are hard pressed to occupy many parts of cold Canada. There's some examples on what you can do with them here, like Ice and Mice. If you really want a Great Plains domesticate, try elk! Highly cursorial, highly social, highly adaptable, highly generalist feeders, and they're already farmed here IOTL. You can ride the bulls (semi-castrating them like reindeer so they still grow large but don't experience rut aggression is a good idea), but selective breeding is required to get the cows from pack to riding animals. It may also change behavior so that bulls tolerate and maintain their bachelor groups longer.
Well, they DID use them for pulling travois. Add wheels, and voila.
Sleds, too; the Inuit weren't the only ones. They were common in parts of the northern U.S that froze during winter.