In my opinion, it is very important for MBA students to use professional pictures on Facebook, Twitter, LinkedIn, Youtube and so on. As they say, "Dress for the job you want and not for the job you have!". I have seen some students who are extremely professionally dressed at all times and then, I have seen a few who do not take formal dressing too seriously.
W.r.t. the grooming and self-promotion bits, if we can not take care about personal grooming, how can we be take care of companies when we are done with the MBA? Now, I know that in some cultures, we are tought to be very modest about ourselves and not to promote oneself. But hey, we MBAs are supposed to be the masters of Marketing. We are supposed to teach the world how to make sales and promotions. If we fail to do that ourselves, it would be a disaster! We need to lead by example and we need to show the world that we are good at what we do. So, in my humble opinion, NEVER hesitate to promote yourself as an MBA student. Coz you will have to do that for your employer tomorrow and for your employer's products and services tomorrow. I wish all MBAs the very best of luck!