JEE

Hi,
There are certain colleges that provide Admission to colleges without the JEE Mains, but they take an entrance test that you need to qualify. You may check the link:
http://www.directadmissionin.in/Engineering/engineering-colleges-in/

It depends that how you perform in written exam and the most important in SSB interview. You need to keep in mind, they are not looking for any scholar, but they are looking for a leader. So, by qualifying JEE, no one can assure you that you would be able to clear SSB Interview. Let me tell you one thing. In a batch of 200 candidates in SSB interview, only about to 2 to 3 candidates were able to make for NDA. Don't worry word hard.
You will make it.

Qualifying marks for JEE Mains / advance varies every year according to the difficulties of paper and no of students appeared for exam and no of seats available. Give your best because there is no fix qualifying marks and also by qualifying only you can't get college. You have to score good marks. So try to score more than 180 in JEE Mains and try to score more than 40 - 50 % marks in advance.

No , punjab university conducts its own entrance exam for admission.

BIT Mesra offers scholarships to meritorious students based on their performance in JEE Mains. For details please visit https://bitmesra.ac.in/Show_Admission_Page?cid=1&deptid=11&pid=14

Sorry but no, you have to qualify the JEE exam or sit in the PET exam for the admission.

Your OBC - NCL will get cancelled during counselling at reporting center and you will get seat according to general cutoff. You will be treated as general student. No need to worry. They will change it at reporting center when you don't have the caste certificate or not valid one.

No, JEE is not required, admission is merit based.