Chemical Engineering

No, LIT, Nagpur does not provide chemical engineering via lateral entry, for the list of available courses check out the link below:
https://www.shiksha.com/college/laxminarayan-institute-of-technology-Nagpur-24822/courses/be-btech-bc?ct[]=156.

50 percentage minimum is the percentage required in 12th.

Frankly, you should get above 160 marks.

Atleast 95 percentile is needed to take admission in the top colleges.

Yes, you are eligible for the same. You may check admission criteria of the college to proceed into the Bachelors. Also, JEE score is important.

You need to clear JEE Mains to get admission in this college and course.
Age Limit for JEE Mains 2019: Candidates whose date of birth falls on or after October 01, 1994 are eligible to appear for JEE Main 2019 Examination.
If you have the age according to the above mentioned criteria then you can appear for JEE Mains and then get into this college
For more details, check out the link below:
https://www.shiksha.com/b-tech/course/b-tech-in-chemical-engineering-indira-gandhi-institute-of-technology-igit-orissa-other-191568.

Yes, for M.Tech in Chemical Engineering eligibility criteria is 60% or above in relevant discipline at Graduation level. For more details kindly go through University website or this link:
https://www.galgotiasuniversity.edu.in/m-tech-in-chemical-engineering.asp

AICTE approval is not necessary if you are studying in a deemed university or in a campus of university (not in its affiliated colleges) approved by UGC, then even if your course is not approved by AICTE, it will not create any problem. So deemed universities/universities campus does not require any AICTE approval before and even after year 2013.

Try to go for full-time proper engineering course. Have a look at the best Engineering colleges in Madurai:
Velammal College of Engineering and Technology
St Michael College Of Engineering and Technology
ULTRA College of Engineering & Technology
Thiagarajar College of Engineering
Vaigai College of Engineering
PTR Engineering College
Solamalai College of Engineering
R L Institute of Nautical Sciences [RLINS], Madurai
Mangayarkarasi College of Engineering
Latha Mathavan Engineering College.

There is no M.Tech in USA. It is called MS there, attempt GRE and TOEFL make your CV strong, then apply for the Universities in USA. All the best.