Engineering

Roorke College of Engineering is better than Shivalik College of Engineering due to various factors. Plus, CSE in Roorke College of Engineering is high standard due to collaboration with some reputed and globally recognized companies. Plus, the faculty, environment factor and the location also plays an important role. Placements are also good.
Good Luck.

You can check the below link for colleges based on ratings, student reviews, fee, infrastructure information. Check the below link for list of colleges in Maharashtra for B.Tech in Aeronautical Engineering-
https://www.shiksha.com/b-tech/colleges/b-tech-in-aeronautical-engineering-colleges-Maharashtra

As per last year trends, I could find Indian Institute of Engineering Science and Technology, Shibpur. You can check the below link for colleges you can expect based on your JEE score-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Yes, you can appear for TANCET exam even if you have arrears. By the time you graduate and apply for other institutes for PG programme ensure that you clear all and then apply.

Yes, for B Tech only 50 percent mark required (general), for others 45percent, according to JEE. For some private university mark doesn't matter. Don't worry you will get a seat.

It is quite possible, you may get seat in second or third counseling, best of luck.

Indian Institute of Technology Dharwad Offers B.Tech in Computer Science and Engineering Course - Four Year Course which is best in Course Delivery and Placements are also good.