Chennai

Yes, you can get admission in either EEE or civil branch in Coimbatore, Bangalore or Chennai. Your rank is enough to get you a seat. You should participate in the counselling process.
Best of luck.

MT Educare and KS Academy are good options.

He can get in aeronautical engineering, if the fees the list think so is only for 100 students.

Students who wish to pursue M.Sc and MA programs must hold a Bachelor's degree in relevant discipline from a recognized board. For admission to Integrated B.Sc + M.Sc program, candidates must have passed Class 12 or equivalent from a recognized board with Mathematics and Physics as compulsory subjects.
Admission to PG courses available in the college will be granted based on Merit in the Bachelor's degree examination.
It has been released already. Check it here https://www.shiksha.com/college/women-s-christian-college-college-road-chennai-23597

Please visit this link this is college predictor hope this will help you
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

Yes, Maths is always compulsory if you're opting for B.Com (Hons.) otherwise for B.Com (programme) it is not compulsory.

Yes, you will get seat for BE.CSE course Chennai at Tamil Nadu. Also, follow this page to check your score and eligibility details more better.
https://www.shiksha.com/tags/jee-mains-percentile-tdp-847953
All the best.

Hi,
With 136/200 marks in NATA 2019 and 63% in your 12th, you have a fairly slight chance of securing admission in Thiagarajar College of Engineering Madurai, for architecture.

Hello Santhya,
Best colleges in Chennai for doing B.Com, you can find college in below link: https://www.shiksha.com/accounting-commerce/colleges/b-com-colleges-Chennai
All the best.

Here are all the details:
https://www.shiksha.com/college/presidency-college-Bangalore-hebbal-19396.