Physics Spl

Yes, students with science background can apply for BA (Hons) in Shanti Niketan.

If you don't want to go to DU then there are other options like IP University and Ambedkar University. These are state government universities while there are central universities also like Jamia Millia Islamia, JNU ( No. 2 rank in India) and for correspondence, IGNOU.

You can give entrance exams like IIT JAM CISR-NET, etc. If you get selected, you can do your Masters. Some institutions also prove integrated Ph.D course.

Mechanics - Klepper
Mathematical Physics - HK Das
Optics - Ajoy Ghatok
Waves - NK Bajaj
Along with these books, you can refer HC Verma, Feymann lectures. Also various edX, Coursera etc. Online learning platforms might help you. If you follow these books, not only they will help you in your college exams, but also in your entrance exams. These books are recommended for every physics student in India.

If you belong to General category, then I am sorry to say you don't. If otherwise you might have a chance :). Here is a link of the previous year cut-off list of DU. Go through it once. http://www.du.ac.in/du/index.php?page=cut-off-2017
Hope this helped :).

Basic 10th and 12th syllabus in physics and chemistry should suffice.

Please check for your eligibility to appear for the NIMCET from the criteria mentioned at the link provided below:
NIMCET 2018 eligibility criteria: https://www.shiksha.com/university/national-institute-of-technology-durgapur/exams/nimcet
Regards.

Yes, definitely, you will got an engineering in any state, as per your JEE marks.

If you failed, then you cannot do that course. You have to clear all the subjects in which you failed. You can repeat your all three subjects. Thank You.