Oh, there really is no need to bring Nirma washing soap. Non-stick cookware is a must. Getting a few spices and non-messy foodstuff is a good idea. Some sweets for me is a fantastic idea. When packing, keep important papers on your body or in the carry-on luggage, NOT in the baggage that goes in the hold.
Books are very cheap in India.
Yes, that is your biggest concern, but it's no big deal. You'll find a roomie and apartment probably within a day or two of your staying here. Living alone is expensive, so you may not want to do that initially. Do NOT ask for University Housing - just ignore that letter when it comes in. We could find you an apt., but we don't know what exactly you are looking for.