Can I get admission in NIU for BSc with 60% in Class 12th?

That depends on the student and his/her interests. For example: A student with a PCM background might be interested in pursuing AI as a subject can opt for a BSc AI & Machine Learning degree. 
Whereas another student from PCB background might be interested in microbiology can do a BSc Microbiolo

No, Nirma University BA LLB (hons) eligibility criteria does not require cadidates to have Law as a mandatory subject in Class 12 board exams. A candidate's chosen stream or set of subjects in Class 12th are irrelevant for BBA LLB (hons) course's eligibility.

No, law is not a mandatory subject to fulfill SRM IST Kattankulathur BCom LLB (hons) eligibility criteria when passing from Class 12th. Candidates only need to pass Class 12 board exams with a minimum aggregate 60% from a recognised board. Their chosen stream or set of subjects in Class 12th are irr

No, SRM IST Kattankulathur BA LLB (hons) eligibility criteria does not require candidates to have Law in Class 12th. A candidate's stream in Class 12th or their chosen set of subjects are irrelevant to be eligible for this course.

It depends on cutoffs and quota. Getting Polotical Science (Hons) is tough with this score, but you may get English Hons in some off-campus DU colleges.