But ulama does not represent Mexico either--it just represents one part of Mexico. And this would be the late 19th century ulama might spread. Since the game is good for playing indoors, it's possible that someone might be inspired by the game and build on it to create a popular sport. I don't think the actual sport of ulama would spread very far from its indigenous Mexican roots, the same reason marn grook never spread far from its indigenous Australian roots. Like Australian Rules Football, such a sport would be completely divorced from its indigenous roots, and the link with an indigenous ballgame would likely only be known to people interested in the history of it.
Also, ulama is more similar to volleyball than basketball, and curiously, volleyball was invented right down the road from basketball's birthplace in Springfield, MA, in Holyoke, MA, and also by people associated with the YMCA.
The border is somewhat smaller, though, meaning less people needed to guard it and any fences/walls cheaper to build. Not that border security was much of an issue pre-WWII, where the border was very porous and a large portion of border security was devoted to keeping out the Chinese and not Mexicans.
Using the current US Census definition of "Hispanic", I highly doubt any of the states to be admitted from Mexican territory would ever have Hispanics not in the majority. New Mexico TTL, however, would likely not be majority Hispanic.
Not necessarily. Mexico still has some mineral reserves around the border, which will attract foreign investment from the US. Mexico still has significant amounts of oil. TTL's Mexico might be able to avoid the resource curse. If it does not, then it would look a lot more like Venezuela than any Central American state due to the economy's link to oil prices. The amount of foreign investment into Mexico will still be there, so Mexico will still be able to absorb plenty of Central American emigration.