NYC Halal Carts, how do you make the white and red sauces?
I've never tried making these sauces at home, but if were going to try the white one it would be a mayo/yogurt/garlic sort of thing. That second link looks like a good place to start.
The hot sauce is different than the sabrett onions, though. The one truck in particular that I frequent has a hot sauce that is most probably harissa based. I use a harissa at home that comes in a tube (I buy it at Kalustyan's) that is the consistency of ketchup- all you would probably have to do is thin it out with some lemon juice or vinegar. It'll be pretty hot, though.