Exam

Yes, there are certain private colleges which offer M.Sc without PUOCET. And also, you should check DAV College, call them and ask what are their criteria for admission, because if seats are left, they will get you admitted.

You can get the previous year's question papers on the link below :-
http://sscbs.du.ac.in/index.php/contact-us/previous-year-question-papers-bms-bba-fia-entrance-exam

You can go for direct admission there through management quota.

All the branches have a good placement record and CSE would be getting the highest placement. IET lucknow is one of the best govt colleges in uttar pradesh. It provides seats to the top students of upsee.

Yes, you need to score minimum 50% marks at your graduation level exam & score 98+ percentile at CAT to get a call for Personal Interview (PI) from IIMs.

You should try and score 98+ percentile to get a call from IIM for a personal interview(PI). In addition to this you should have scored minimum 50% at your graduation level exam.

Yes, she can appear for the exam at Mumbai, but you have to send a mail regarding this to the Amity University-Jaipur.

It is somewhat difficult that you'll be upgraded to Warangal, as it is the topmost NIT. I'll say, you keep your fingers crossed, and you'll get the best you deserve.