B.Tech Computer Science and Engineering

All Tier 1 colleges are having B.Tech CSE course, that is IITs, IIITs, NITs, BITs Pilani, Hyderabad, Goa, Dubai, VIT, many colleges from DU, Jadhavpur University, SR university, Thappar Institute of Engineering, Chaitanya Bharati Institute of Technology, Jawaharlal Nehru Technological University, and Osmania University.

Yes, a Diploma holder can apply for University of Allahabad for B.Tech CSE.

Yes, you can if you have completed your intermediate with Maths, Physics, and Chemistry. 

Also, you can give some entrance exams for colleges.

With an OBC-NCL rank of 65,763 and CRL 192,901, unfortunately.NIT?Warangal's CSE for OBC-NCL (Other-State) closes around 441–792 in HS and 650–974 in OS quotas. Your ranks are far outside this range, so admission to CSE at NITW isn't feasible. Consider alternate NITs, IIITs, or state/private engineering colleges where your rank fits better.

No. you will not get admission 

Hi, it can be observed that pursuing in Hyderabad can be either too expensive or inexpensive depending on the college and course you choose because about half of these colleges offer a tuition fee of less than INR 3 Lacs and the other half has a fee of more than INR 3 lakh. However you can refer below for the best BTech CSE colleges in Hyderabad  that offer quality education at affordable cost:

Hope this helps!