Engineering

No, you should write exams like CUCET, JAM and PUCET.

Since you got an 19000 rank in AEEE you may have some chance to get admission into Amrita Coimbatore in the state quota for the mechanical branch. Although you will easily get an Aerospace Engineering branch as its cutoff rank is usually above 19,000 rank.

So, you have a chance in Aerospace Engineeri

Unfortunately with your rank and category you do not have chances of getting any IITs. I will suggest you to sit for JoSAA counselling with your JEE Main score, that might fetch you good NITs and IIITs.

EAMCET cut-off for Arora Engineering College varies course to course . Here are cutoff list for few courses-

1. Electronics and Communication Engineering - 81919
2. Mechanical Engineering - 77967

Yes, B.Tech. in Electronics and Telecommunication Engineering is offered by Model Engineering College Thrikkakara Kochi.

Yes, it does offer B.Tech in computer Science and engineering.

Yes, the difference in the name will cause problem in document verification, but it can be solved with a simple affidavit. It should mention both the names of your father and should declare:

That both these names pertain to the same person

That it is true to your knowledge, and

That you're accountable

It's difficult to get any government college with this percentile but here are some colleges for which you can try- 

1. Keystone School of Engineering, Pune
2. KKEI'S Trinity Academy of Engineering, Pune.

Both of the institutes are very prestigious and good in their own terms.

ANITS has a great campus land of 12 acres. It has good infrastructure and is an autonomous college. This college is approved by NAAC, NBA and AICTE. The fees for this college is 3.6 Lacs for 4 years. The placements are also dece

As It is mostly depandent on 12th percentage and JEE main mark (sastra will calculate like this 12th percentage * 0.75+jee main mark * 0.25)

As you have already got 98.6% in boards, hopefully you will get CSE in Sastra University.