Guru Gobind Singh Indraprastha University

The following Colleges offers B.Tech lateral admission in B.Tech CSE.
1. Delhi Technological University
2. Guru Gobind Singh Indraprastha University, Dwarka, Delhi
3. Dr. Akhilesh Das Gupta Institute of Technology & Management, New Delhi
4. GL. Bajaj Institute of Technology and Management, Greater Noida
5. Amity University, Noida.

Yes, NIOS class 12th certificates have the full validity at par with other boards like CBSE, ICSC, etc. So, you will get admission in asked colleges in B.Tech courses if meeting the other requirements.

No, Mathematics is not necessary in class12th for B.Com (Hons. ) of GGSIU. The eligibility criteria for B.Com (Hons. ) of GGSIU is given below. Eligibility Criteria: 50% in aggregate in 10+2 examination / senior school certificate examination of C. B. S. E. as minimum marks for admission to B.Com with pass in five subjects (One language and four elective subjects) or an examination recognized as equivalent to that. Admission Criteria: Admission shall be on the basis of the merit of the written test /CET.

Yes, you have to participate in LE. B.Tech (Diploma) entrance exam (CET code no. 128) for taking B.Tech lateral admissions in Guru Gobind Singh Indraprastha University and its affiliated colleges.

Sorry to say, but you will not get any college on the basis of your NATA and JEE Mains paper 2 scores. The reasons are:
90+ marks are considered as NATA cutoff for various government colleges.
300+ marks are considered as JEE Mains paper 2 cutoff for NITs and government colleges.