Let me give it a try:
1. Life at HHL
I like it a lot. Since HHL is still a very small business school (500 students), you will get to know almost everyone on a personal level. Chances are high that even the administrative staff will know who you are after a couple of months. Furthermore, there is a strong "HHL spirit" among the students.
Coming from a non-traditional background, I have learned a lot during my first 5 months here. However, I must also say that the workload, especially in the first term, is very high.
One thing that can be a little bit frustrating is the sometimes low work attitude of some exchange students.
2. Student diversity.
Concerning nationality: High. I think we have 9 or 10 different nationalities in the current batch, whereas Indians and Germans represent the highest fraction.
Concerning background: High. We have students from various backgrounds. Let me just mention a few which come into my mind: Banking, VC, Consulting, Academia, Chemical Industry, Telecommunications, IT
3. Alumni network.
Still rather small (HHL was brought to life again in 1992) although I don't know concrete numbers.
Nevertheless, HHL alumni are usually easily approachable. There are numerous events where alumni come back to HHL in order to recruit, especially within the consulting and start-up sector. In case you want to apply somewhere (in Germany), it is very likely that there is at least one HHL alumnus working there. For you, this means that the career center can put you into contact with this person.
4. Have you seen any entrepreneurship activity on campus.
Lots. There is s start-up career fair once or twice a year. Besides, there is a student initiative called "accelerate" which focusses solely on entrepreneurship. They organize a start-up conference which takes place every year. Furthermore, you will most likely see at least 2-3 HHL entrepreneurs giving talks at HHL. Finally, I know of 2 VCs headed by either HHL alumni.
5. Job prospects as compared to West Germany.
Concerning job prospects, the West is still ahead but the East is catching up. For example, Porsche just built a new factory in Leipzig and Zalando a logistics center. Besides, Berlin and its huge start-up scene is just 2 hours away.
Of course, if you want to work in finance, Frankfurt is still the place to go but bear in mind that Germany is tiny in comparison to India. ;-) You can easily reach every city in Germany within 5 hours and you certainly not limited to East Germany. In fact, I know of some M.Sc. people (they have to do their internship from Jan-Mar) currently doing their internships at IBs in Frankfurt.
6. Quality of education.
Good to excellent. Of course, it always depends on the lecturer and on your expectations. But in general, I can say that HHL offers a nice mixture of HHL professors and externals offering classes. Usually, external professors are from well known (business) schools around the world.
7. How are the Professors (I did talk to Prof. Velamuri and it was encouraging)
In general very nice and approachable. Some are stricter than others (usually, the German profs are on the stricter side ;-). Of all classes I've had so far (something between 13-15), There were 3 classes so far I did not like too much. In my opinion, all the others were really good.
8. Social life at Leipzig.
Compared to Mannheim: Way better. I have lived in several German cities so far, and Leipzig is my favorite by far.
9. Expenses at Leipzig for an average student.
Leipzig is very cheap, especially if you compare it with West Germany. You can easily make a decent living with 800-1000?/month if living in a small appartment. Of course, this always depends on your living standards.
I hope I answered most of your questions to your satisfaction. As you might have inferred from my post, I am very happy at HHL.