Government & Defence Entrance Exam

Yes, you are eligible. UPSC eligibility criteria says you need to pass your graduation. That's all.

IITJEE is difficult to clear it. Selection in IIT JEE is based on written exam only while that in NDA is based on written + 6 days SSB Interview + Stringent Medical Test. IIT JEE does not test a candidates leadership skills but NDA does. The no. Of seats in NDA (around 320) is much lower than IIT JEE. Although candidates appearing is also less.

Yes, you can go for IAS if you have bachelor's degree in any stream. After B.A.LLB, you can easily go for it.
All the best

Do you really think that joining a coaching institute can help you out to crack the IBPS Exam? What if I say that you can easily crack the IBPS Exam without any coaching institute!
Yes, it is possible. You just need to follow some simple guidelines for it. Check out the study plan that can help you to crack IBPS SO Exam without any coaching here - https://examsmode.blogspot.com/2019/04/how-to-crack-ibps-so-without-coaching.html Click to read. Still, if you want to join any coaching institute in Patna, then check the reviews of the institute and then apply for it.
Best of luck!

Rau's IAS Study Circle
Chanakya IAS Academy
Sathya IAS Academy
Brain Tree India
are some of the top IAS coaching institutes in India.

The details of the exam center will be mentioned on your admit card.