B.Tech

If you can wait for special counselling from IPu that happened later in the month of September, you can't get in MAIT also (even batch).
As of now, you can get in Surajmal, still, I will advice to go through the last year cut-off for a clear knowledge.
All the best.

BA (Hons) [H&SS]-40 seats [fee 5000 per semester]
2-B.Tech [IT&MI]-40 seats [fee 5000 per semester]
3-MME-20 seats.

To get admission into ANITS, simply take EAMCET exam conducted by the Govt. of Andhra Pradesh. You can even get a seat if you couldn't attempt the exam. Please visit this link for further information, cut-offs, etc.: http://www.anits.edu.in/
http://www.andhracolleges.com/colleges/college-profile.aspx?clgid=EN026

Passed or appeared in 10+2 Science/equivalent with P.C.M. 45% marks in aggregate (Minimum requirement of 40% marks is applicable to reserve category candidate)
Course fee: 5 lakhs.
The JEE cut-off varies each year. You should obtain at least 75 or above.
Good luck.

SRM Institute of Science and Technology, Chennai
Indian Institute of Technology Madras
SASTRA University, Thanjavur
Amrita School of Engineering, Coimbatore
College of Engineering, Guindy
Madras Institute of Technology, Chennai.

I shall respond to the Second Question First. The Placement Status of IITs is the best in the country. It is not just about the number of people. Places or the total percentage of placed students. It is more about what kind of Jobs are offered and achieved. IITs get good jobs and salaries. Now, The B.Tech and M.Tech aren't placed together. They might sit in the placements but because of the qualification there remains a difference in the realised offers. The students do have the choice of picking a job but the degrees are surely different for the employers.

Open Fee Waiver Category.

Yes, you will easily get admission.

Yes, you can get admission.