My wife did not get her name changed, so I might not be aware about
exact procedure. In our case too, we wanted to avoid unncessarily
paper work and waste/kill time in applying for her new passport that could come along with the changed name.
1. Mumbai counsal is better than Delhi at least as far I have heard. "Money wasted, time wasted, energy wasted..." Sorry but is normal if you apply to German embassy (especially for family reunion) in India.
2. In Delhi they expect one to pass the exam and show them the passing certificate on applying (at least in 2009). So I doubt if it is possible to apply simultaneously.
3. If her passport in still with median name, then I do not understand how you wrote earlier "that she took your name"? Did she got her name changed on her Indian ID-card, voter ID card etc..(which does not matter much for consul, untill you dont show them) Is her changed name mentioned on marriage certificate?
4. Never heard of some special category, but yes if your wife has done Masters, then the chances of excemption from German course wer high in 2009 in Delhi.
All the best!! Do not lose patience and keep struggling. Its matter of time (unfortunately runs in weeks)