B.Tech Computer Science and Engineering

No, you cannot get admission in any good government college. You can apply for top private colleges. Otherwise, you can try in state level government college.

Yes, you can get a seat in IIITs.

AP-EAMCET 2018 College Predictor:
Use your AP-EAMCET 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of AP-EAMCET 2017
Get resources & insights on colleges & courses
https://www.shiksha.com/b-tech/resources/ap-eamcet-college-predictor

Enough seat are available in LPU, go and get admission. In LPU, there are 10-25 sections of branch, so admission will be easy, if you have good marks in class 12th.

Please specify the entrance exam for which you have appeared so that I may be able to populate relevant details regarding your eligibility for admission.
Top computer science engineering colleges in India are mentioned at the link provided below. The ranking is based on engineering ranking published by The Week.
https://www.shiksha.com/b-tech/ranking/top-computer-science-engineering-colleges-in-india/46-2-0-0-0

There is no difference in B.E. And B.Tech.Syllabus remains same for both. I think, you should go with CSE. It has a lot of scope in multinational company.

There are over 13 B.Tech colleges in Gwalior Offering 103 Courses. Please refer to the link provided below for a detailed list of these colleges. You should be able to navigate to the best colleges on this list using the filters on the web page. Regards. https://www.shiksha.com/b-tech/colleges/b-tech-colleges-gwalior.