I'll try to do this by memory, but honestly I haven't looked at the scenario since it came out, so this may be wrong. So take it with a grain of salt.
1). It is recommended to only play the Sandbox version, since the non-sandbox version never was completed. This will give Mexico a free choice to whomever they want to join.
2). I don't recall if horses can transport infantry. Bombur would have to weigh in on that. The reason that some units show wheeled for instance, is that the game always takes the least favorite movement type for a unit. If there is mud, then that can quickly turn into wheeled. However sticking to roads should still give the infantry movement rate. SO don't worry, it is WAD, although the type of movement on the counter may be a bit off.
3). You can choose weather or not, depending on your preference. There is no bug in the weather system that I know of. There are however other bugs. Twotribes is the one who knows most about which there are at present, since he plays it (often?).
4). If I recall, changing it to personality makes it harder to guess what it will actually do. Some times the AI for a nation will be aggressive, sometimes more passive.
In any case good luck with your game. It is, I think, a good scenario, although I strive for excellence.