Lateral entry

IEM takes admission through WBJEE and JEE Mains and not through any other joint entrance examination. Your rank should be between 700 to 800 (GMR) to get into IEM. IEM offers 12 seats for mechanical students through JELET. Usually, if seats get vacated at the end of the first year and there will be

Dear,
Yes, you can get lateral entry admission to BCA in some universities after doing Diploma in engineering.

No, it's not at all possible because your score is not so good at least minimum eligibility is needed. As CSE is a very demanding course it's not possible for you to take that branch. You better choose any other.

No. There is no lateral entry for IITs and also for NITs.

For this rank, it may be difficult to get government seats in DSCG if you are from general category. If you have a reservation then you may get government seats.
Good luck.

In respect of reservation of seats for SC /PWd and various other categories, seats varies according to the government of West Bengal rules of the concerned university, prevailing at the time of admission will be followed. Such reservation are only available to West Bengal Domiciled candidates. And,

I think distance learning is an option for this type of situation. Sikkim Manipal University is one of the best institutes for this. Kindly check the distance learning programme of the universities.

For technical courses AICTE recognition is must
For non-technical courses UGC recognition is must, as simple as that. If you are studying engineering, Diploma, see your college affiliated to AICTE, if you are doing BA B.Com B.Sc. See UGC recognition.