Colleges in Bangalore

For travel and tourism, we have integrated 5 year program MTTM master of travel and tourism, UG and PG integrated.

Yes, students from any field can join law and NIOS is a valid board hence you can take admission in MS Ramaiah College of Law

Admission in B.Tech LE programmes offered by engineering institutes is done on the basis of entrance exams. Different institutes consider different entrance exams. Most of the regional government and private colleges take admission on the basis of state entrance exams.
Some deemed universities and autonomous institutes might conduct their own entrance exam for admission to B.Tech LEprogrammes offered by them.

Yes, you can take admission

You can definitely opt for PGDM.

Kindly refer to the link below for best colleges in Mumbai
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-Mumbai-all/2-2-0-10224-0.

You are already pursuing B.Tech course then why do you want lateral entry admission?
Lateral entry is only applicable for Diploma qualified students.

You can refer to the student reviews and decide if the college is good or not https://www.shiksha.com/college/vogue-institute-of-fashion-technology-vift-richmond-road-bangalore-440.