Mechanical Engineering

Both branches are very good, but it all depend upon your work interests, but going with ME there are more advantage than chemical engineering.Go through the link:
https://www.shiksha.com/b-tech/articles/what-mechanical-engineers-learn-blogId-3657
https://www.shiksha.com/careers/chemical-engineer-134.

As a mechanical engineer I would suggest you to go for chemical engineering, if you are not good in drawing, because in ME you have to face engineering drawing, mechanical engineering drawing, and basic engineering drawing.
You will face very difficult in tackling these subjects
Good luck.

the lateral entry is on the merit base ,
for more details about the admission process
you can follow the link
https://www.shiksha.com/college/dwarkadas-j-sanghvi-college-of-engineering-vile-parle-west-mumbai-19969/admission

Yes, you can take admission in this college.
For more details about the admission process:
https://www.shiksha.com/college/st-mary-s-technical-campus-barasat-kolkata-42646/admission
Kindly follow the link.

Here you can find all the courses fees along their admission parameters
https://www.shiksha.com/college/sirt-sagar-institute-of-research-and-technology-bhopal-54731

Hi,
Here are the list of some top college providing distance education in Chennai
https://www.shiksha.com/b-tech/colleges/distance-correspondence-b-tech-colleges-Chennai
Just follow the link.

Kindly visit this link:
https://www.shiksha.com/b-tech/ranking/top-mechanical-engineering-colleges-in-india/48-2-0-0-0

You can do Bachelor of Engineering via distance education programme. Here is the list of the colleges:
https://www.shiksha.com/b-tech/colleges/distance-correspondence-b-tech-colleges-india