Engineering Entrance Exam

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.

If PCM score is 50%, then you can get admission in ICEM. Your JEE score is less, so you can apply for the direct admission process.

Yes, it is compulsory to clear cutoff of every subject to clear JEE advance. You cannot qualify JEE advance with the help of one or two subjects. The cutoff of every subject is class 12-14 marks per subject, which can vary depending on the cutoff.

JEE Mains No. Of Attempts:- The exam authorities have set a rule regarding JEE Main 2018 Eligibility Criteria that the candidates will only be able to appear in the exam for 3 times. This means that any candidate can avail only 3 chances to give the JEE Mains Exam. Regards.