Recreating New York street vendors' "halal chicken over rice"
My guess is that the chicken is a variation on chicken kebabs. These are often made by marinating the chicken in yogurt with garlic and turmeric. The same technique can be used for chicken on the bone. 

I'm not sure for the rice -- maybe someone else can help out?

The hot sauce is most likely harissa. This is a generic term for a number of spicy sauces used in the middle east and northern Africa. The basic recipe is dried chilies, other spices, and olive oil. Here are some variations. 

There is also a Yemenite hot sauce known as skhug or zhug. (It may also be known in Israel by the generic name Harif, which means spicy or sharp. Note the same root as Harissa.) This can be green or red or even brown, depending on ingredients. Green zhug is often made with cilantro, while the brown one includes tomatoes. The red one includes red peppers.  

The white sauce is probably a variant on yogurt sauce, such as labneh. This is often combined with garlic and a green herb such as parsley.