Engineering Entrance Exam

There will be no influence of 12th marks on your MHCET 2017 scores.
There is a criteria though in which you have to score at least 50% in your 12th for validation of your MHCET Scores.
If you don't satisfy this condition of more than 50% marks, your MHCET scores are not valid and DTE does not issue a scorecard for your marks.

You can sit for JEE exam but you cannot apply for counselling of NITs. As per the JOSAA scheme, you need atleast 75% in your 12th to be eligible for the counselling of NIT's.
Hope this was helpful.

In which state are you looking for CS?

B.Tech is a good course because it is a professional course and B.Sc is a Bachelors course with good job opportunities.

For Mathematics, you should follow R.D.Sharma.
For Physics, you should follow D.C.Pandey
For Chemistry, you should follow NCERT Textbook.
Best of Luck and Work.

AAT exam is for you to get into IITs to pursue a course in Architecture. There is, of course, not any compulsion if you are not interested in B.Arch, whereas, JEE Advanced is for students who are interested in pursuing B.Tech from IITs.
Hope this was helpful.

Chances are very less, for getting admission in LNMIT, but still apply for it.

No, it's not possible. Try for other NITs. To know the opening and closing ranks of JEE Mains, follow the link josaa.nic.in