NIT Trichy - National Institute of Technology

Its hard for you as you board score is less. Also depends on your current year percentile in boards. You might get in new NITs though. NIT-T, NIT-K etc will mostly not available to you. Also it'll make a huge difference if you are from a reserved category.

In India, the best is Institute of chemical technology,Mumbai. With you jee marks its really hard for you to get admission in NITs. If you are from a reserved category you might have a chance.

105 is the last year cutoff for JEE-mains.

The total expenses for tution fees per year will be Rs 114,000 per annum which includes all tution , library and etc . For hostel and mess includes Rs 53,000 per annum

There is no point giving a false hope. I would suggest start looking for admission in premier private universities like BITS, MU and Lovely Professional University etc.
Taking a drop would not be a logical step as gap year affects your career a lot.
Dont worry on the placement or Education part. If you would be good you would obviously do well. Best of Luck.

The fees is almost double for NRIs

Jee main 220 aboveBoards 96% CBSE will definitely be enough for general other state.

Can you be specific about which NIT.

There have been cases where a genius makes it through with going for coaching but I would say it is mandatory for a normal student.
A coaching class is trained to study the exam characteristics and have professional who can take you through the process is a well guided way. They also provide you with materials and experts to approach and since everyone avails it now. I believe it is a necessity. It is a decent investment for a bright future.

For fresher minimum package is the lowest it is around 5.75 and there are fresher people who got 8lpa