Lateral entry

Lateral entry in graduation is provided to mostly Diploma holders and also sometimes to other degree holders. You can get admission in the second year directly via lateral entry. You will have to pass some subjects of the first year though.

You will have to apply for WBJEE JELET to get admission in Jadavpur University. You are eligible as you have Diploma. Check whether you have minimum marks or not.

This may not be possible as your percentage is not that good so, it cannot be guaranteed but, yes you can apply. You may get admission.
Good luck.

Yes, you can take admission in engineering in any department.
Almost, all the colleges accept lateral entries, but a few of the most reputed colleges like IIT, NIT and VIT do not encourage lateral entry.

Singhania University has now been granted the approval to conduct AME course as a regular Bachelor's degree. Hence they have started offering a Bachelor's degree i.e. B.Sc in AME. Only those candidates who have qualified TSICET-2018 and secured 50% (for OC) and
45% (for others) in aggregate marks degree or its equivalent examination can apply for this. Hence your degree qualification should be acceptable and you may get admission provided you score the minimum required marks in the entrance exam.

Yes, you can. Approach the college without wasting anymore time. Admissions will close soon everywhere.

Please refer the link: http://ipu.ac.in/usict/Scheme_Syllabus.php.

This page has the information you may need:
http://jnnce.ac.in/old/o/admission12.htm

No, you may have to take WBJEE for that and you will get a seat only if there are seats available. There is no other way.