B.Tech

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=8030745
Check the above link for colleges you may expect. It will be difficult to get NITs at this rank. You can look for other state engineering colleges accepting JEE Mains score.

Sorry, but you can't get admission without EAMCET, but I think this college has a management quota, you can get admission via management quota. For management quota, you have to talk to the college officials.

Different branches have their own unique advantages and different job opportunities. The most highly paid sector in terms of Engineering is Oil and Petroleum department. If you manage to get a job in this sector, your payment might be a bit high compared to an average engineer. But, that too depends on your profile and skills.

CS is better to join as compared to EL.
However, you may get a chance to get CSE if performed well in 1st year at BITS.

It is Tamil Nadu Engineering Admission exam. The registrations will start from 3rd of May.

It may depend on the college, but the average fee is around 5 lakhs.

As MSW is a Master's degree program, any graduate can pursue it. However, it is important that you check your interest after MSW.