BDS

I don't think so. In government officers, it is not possible at all.

BHMS is better than BDS because there are not many cases of teeth problems of people in a society but BHMS is preferred by many people.

BPT and BAMS. Both of these have good scope and salary.

Both are best in their own way as both are different. If you want to became a dentist, then go for BDS and if you want become a good homoeopath, you can go for BHMS.
All the best.

Yes, Manav Rachna Dental College is one of the flagship institutions of Manav Rachna Educational Institutions (MREI).Manav Rachna Dental College is NAAC "A" grade accredited, recognized by Ministry of Health and Family Welfare, Government of India, Dental Council of India and Government of Haryana and affiliated to Pt. BD. Sharma University of Health Sciences, Rohtak (Haryana).

You can prepare for NEET by taking 1 year drop. And remember graduation is must for any further exam since it is the basic criteria. You can go for BDS, BHMS, etc.