Engineering Entrance Exam

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No, your score is very low. You will not get any government college but you can try for private colleges. There are some private colleges which are actually good. Don't lose hope. You can drop a year for JEE Mains and Advanced. You have many options.
Good luck.

If you have done 11th and 12th level PCM decently, you will be able to solve most the questions in the 1st paper.
In the second paper about 40 MCQs had to be answered in 1 hour (negative marking was there). The difficulty level was way higher than what comes in WBJEE.
The difficulty of question papers in competitive exams doesn't matter much. What matters is how you were able to perform in that paper than the rest of the other competitors. Practice is the key.

It is basically a version of the SAT that's scaled down for an Indian student(the English part). It is found pretty easy though. It's neither too tough nor too easy. Just the right level of English and aptitude you are expected to have at this level.
Yes, definitely, if you do well you will get this college.

No, you will not get CSE with this rank. You will not get any top branches like mech, ECE, civil, chemcial, etc. You will only get construction and power engineering. For more details, click on this link :-
https://wbjeeb.nic.in/wbjeebcouns/orcr/PrevYearORCR.aspx.

Yes, absolutely.

You cannot get Heritage with this rank. Try for Techno India or Haldia or MSIT or NSIT. For more details, click on this link:-https://wbjeeb.nic.in/wbjeebcouns/orcr/PrevYearORCR.aspx
Here all the details are available for all the colleges which are under WBJEE.