CBSE 12th

Yes, you can apply if you have interest and if you want to grow in the sector of environmental science.

Your profile seems quite decent to me. With a really good CAT score you should be able to get a call and from there it would depend on the interview. By the way, you didn't mention your graduation college, because that would also make a difference. Do also look at XLRI and FMS, I feel you would find the experience better for your background.

Go for direct engineering like BE/B.Tech. Don't go for Diploma. Diploma is chooses basically when you have no chance to get admission in B.Tech programme or those who are going to waste their year.
Diploma is better to pursue when one chooses it after10th, not 12th. Go for B.Tech or BE.

No, the results are valid only for a year.

It depends upon the cutoff which has not released since the result is not announced. The result will be coming on 30th April 2018. After this the cutoff for the different categories will be announced. Then if you do not attain the minimum score then you will not get any college but if you have qualified with above minimum marks then it might be possible that you will get the college.

No, only science background students can do engineering. You can do polytechnic Diploma.

Go and take admission in Thakur College of Engineering and Technology. Even their fees is high as compared to others but the facilities they provide are well and good.

JoSAA Eligibility -Criteria for JEE Advanced 2018
Candidates should have successfully qualified JEE Advanced 2018 examination. The candidates should have scored at least an aggregate of 75% marks in their 12th standard qualifying examination. SC/ ST/ PwD category candidates should have secured aggregate marks of 65%.

If you are from CBSE board then you must follow NCERT for board's exam. CBSE makes the exam on the basis of NCERT only. Must do the hard work solve the previous year question and concentrate to studies. Just focus on your studies only.