Alternative Medicine

Yes, BUMS B.A. MS BHMS BVSC. are also included in NEET.
Here is the cutoff of above-
BAMS:- 480+
BHMS:- 420+
B. V. Sc. :- 380+
BUMS:- 330+.

Yes, you will definitely get admission in B.A. MS or BHMS through your State quota in your respective state. So, Congratulations for your medical career ahead.

Yes, NEET exam is compulsory for admission to medical courses, including B.A. MS Candidates must qualify for the NEET cut-off for B.A. MS and percentile has declared for that particular year. The age limit to pursue B.A. MS courses is 20 years for the general category whereas 24 years for the reserved category. For BHMS, it is also compulsory to give NEET as most of the College makes their Merit list based on NEET marks.

I think it would be difficult to get admission with these marks. You need to score atleast 400+ to be on the safe side.

For getting admission in BAMS in this college, you need to score atleast 480+ marks in general category and for OBC it is 460+ and SC & ST is around 390+. You rank should be in range of 50-70K for getting admission in this college.

https://www.shiksha.com/university/amu-aligarh-muslim-university-29839/cutoff
Here you can get your answer.

No, we can't do it after the BHMS course.

Yes, you are eligible for BMLT/BMLS course after completing DMLT or Diploma in MLT. You can get lateral entry (admission in 2nd year) in B.Sc. MLT.

Homeopathy is better
https://www.shiksha.com/medicine-health-sciences/articles/how-is-allopathy-different-from-homeopathy-blogId-38367 here you can see the difference.