Engineering Entrance Exam

Not sure about your CET score but you can get chemical engineering with help of your JEE Mains marks.
You need to wait for 2nd or 3rd CAP round. Hope this will help you. You can ask if you have any queries in comments.

These are the certificate which will be given:
B.Tech (CSE)/B Tech (ECE)/B.Tech (Mechanical Eng)/ etc.

There are two options available for you-
1) You may opt for private colleges like VIT or SRM (if you have enough money).
2) You may think of taking drop and work hard to get better next year.

Yes, a lot of jobs are there. Only you need a degree. Based on your degree, you will get the job. For example, if you will do electrical engineering, you will get a job related to electrical like machine works and all.

Yes, you can. So, start preparation for the GATE exam.

https://www.shiksha.com/b-tech/resources/upsee-college-predictor
Please go to the college predictor link, I am sharing here to know about the college you can get. Good luck.

You can use this link to check out your chances of getting this college. This is shiksha's official college predictor tool based on previous years data. Hope this helps. All the best.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_campaign=6375912

No, you can't not even if you have internationally published and recognized projects. They want GATE. I don't know if it's an IIT thing or an MHRD thing but a person who spends most of his/her day doing really good projects has little time to prepare for exams like GATE and are usually not the type who sit idle and study for an exam for a year after finishing their degree.
So if you're bright, a hard worker, and doing good research/project work, in India you are out of luck.