Colleges in Rajasthan

It depends on the course you choose, and the caste you belong to. So, be more specific.
May be in CVR, you can get a course you want.

As per of my knowledge, you can't do this.
Lateral admissions are for Diploma holders.
And in 2nd year, if you score good marks, you get a chance to change your branch (if you are willing to do so).
And if the seats in MBM will be left vacant they will give an advertisement in all the newspapers inform

No, there is no entrance test conducted by Jaipur National University for B.Sc. Shortlisted candidates are called for personal interview based on marks obtained in 10+2 level. Candidates are selected based on performance in personal interview. Interested candidates can apply online/ offline with the

Yes, you can do M.Sc in Big Data Analytics after completing B.Tech. On the basis of percentage of last year, you will get admission.

BITS does not offer lateral entry scheme.

As per the cut-offs, there are no chances.
http://www.bitsadmission.com/cutoffscores2017.aspx