Colleges in Rajasthan

BITS, Pilani does not offer degree course in the field of architecture.

Yes, you can but for that qualify JEE Mains with a good rank. As you are from Delhi, apply to Delhi colleges like DTU, GGSIPU, IIIT, NIT, NSIT through JEE Mains instead go to Rajasthan as you have 85% Delhi reservation quota.

BITS Pilani has civil engineering department which is more than 50 years old. Admission is based on BITSAT.

JEE mains is the compulsory exam, which you must take if you want to pursue engineering. If your score is good, then you can get admission in any government colleges.

Government colleges always require a better rank, but your question is not clear. You want to about the rank in which exam, JEE Mains or the state entrance exam. Please state a clear question then only I can help you with the other prospects.

Yes, it is possible. Your need to make sure that your basic concepts are clear and rigid. You can read NCERT books. You can practice questions from other books and do take mocks, i.e. practice questions with timings that will help you to analyse the methods and also in time management.
Best of luck.

Scoring above the border line does not guarantee your admission in a government college. It only provides you an opportunity to take part in the central counselling process. So, you can try to score far away from the border line.