I'll try to address your concerns in order. First, though, make sure you take good care of that ankle. You don't want an ankle problem nagging you all the way to the half marathon.
As for the elevation, you're right to not be concerned. You shouldn't even notice a difference.
As for the actual concerns you list:
1. This is the one to be worried about. You need to do what you can to be prepared for the heat while training through the New York winter. How to do this? First, overdress. It sounds crazy to wear even more than necessary in winter but it's unfortunately one of the best ways we have to heat train. Second, if you have access to a treadmill, use it once or twice a week and don't take it easy on yourself by using a fan or turning down the heat. If possible at least, make it a sweat fest. Again, it may not seem fun but it will help you be ready for the Arizona heat.
2. I wouldn't be too worried about the humidity. The relative humidity in Arizona may be lower but the actual amount of moisture in the air will actually be similar to New York in the winter. As a point of reference, you can play around with this calculator. 10% humidity at 70 degrees suggests an 11 degree dew point, the same as 60% humidity at 23 degrees. The one thing I would suggest you prepare for is making sure you're hydrated. That means being well hydrated before starting the race and making sure you drink enough on the course. You don't have to go to extremes and doing so can actually be more hazardous than being moderately dehydrated but make sure you are prepared to at least take advantage of what is offered at the aid stations.