Exam

It depends on your level of preparation. Factors to consider? One way to know is to take mock tests. You can even take tests online based just on your 11th syllabus, so take a shot to see where you stand.
If you find that you are good at understanding the concepts easily, have sufficient problem-sol

You can apply to the colleges through national level exams like CAT, MAT, NMAT and many more. And there is state level exam MAH MBA/MS CET. You can also apply for this exam and then participate in DTE Cap round process as an AI student to get admission in these colleges.

Please refer to the official website of NIT, Warangal. They have provided the opening and closing ranks of last year's admission.
You can compare your rank and can predict about it. There is no constant cutoff. It changes every year but it is assumed that it will be similar to the previous year.

First of all, which college are you asking for? Because different colleges have different JEE Advanced criteria. Please tell me the college name, then I can explain you branch wise.

Very difficult, but there may be a chance due to domicile benefits. Your rank is 140k, which is not much attractive for a good college. You can get an average college at this score.

You have to pass 10+2 or PUC examination in 2017 with Physics, Chemistry & Mathematics as the main subjects from a recognised board. If you have studied Biology, Electronics, Computer Science, Statistics, etc. in addition to PCM, then also you are eligible to apply.
You have to secure a first class

You should drop for a year if you are confident to crack it. Other wise go to the best private college which provide good education and placements too. There are so many options of the colleges for you. Think about it
Hope this helps you.