New Dehli is quite ok. Traffic conditions is better than Mumbai. Not sure when is the winter but heard it can get pretty cold. So, do your homework on the weather for your entire period.
In India, main thing is be very careful with the water you consume. I brush teeth with drinking water as well. Things like salad and fresh fruits, try to minimize. Since you will be there for 2 months, buy fresh fruits from the supermarket and wash and cut them yourself.
For cars, normally, its better to book the cab for the entire day. And the driver will wait for you. Hotel pricing is on the high side, so do make sure your credit limit is sufficient.
I tend to put on weight on my trips to china and india. So, u might want to do some exercises in your free time there.