B.Tech

You can consider following colleges:
Maulana Azad National Institute of Technology, Bhopal, M. P
Motilal Nehru National Institute of Technology, Allahabad, U. P
National institute of Technology, Durgapur, West Bengal
Malaviya National Institute of Technology, Jaipur, Rajasthan
Dr. B R Ambedkar National Institute of Technology, Jalandhar, Punjab

Of course, you can. There are several engineering entrance exams like:
WBJEE, COMEDK, BITSAT, VITEEE, SRMJEE, KIITEE, etc.
You can also consider private colleges in South India that are even better than some government colleges in the north.

Yes, you surely can do that. Diploma in IT will not help you to start from 2nd year, but it will definitely help you to understand the vast syllabus of B.Tech. But, in my opinion regular courses are always better than any distance course. Good Luck.

If your Diploma is approved by AICTE, then by giving Lateral JEE in Karnataka and securing good marks you can surely get admission or else try management quota. Good Luck.

To be eligible to get admission for pursuing Petroleum Engineering course, you should have passed 12th standard or an equivalent examination with PCM stream or three years Diploma in Petroleum Engineering course from a recognised board/ institution. If you have checked all the boxes written here then you can surely get admission. Wish you all the luck.

No, UPSC provides same type of question paper for all the students appearing for the exam. It does not distinguishes based on your type of degree.

As per last year, minimum percentage cutoff was follows:
General-20%
SC/ST-10%. .

It depends on the college whether it is private, government or semi government. As we know CSE has always been the top branch in Engineering, so you should expect high fee structure. You should try for NIT, IIT colleges.