Government & Defence Entrance Exam

No, you can just ensure that you are fit, just by going for a morning walk and can exercise at home just to ensure that you are perfect. And even practice running. Gym is not necessary as you are going for IPS officer training, not for boxing or something else.

IIT is an Institute to pursue UG or PG programmes upon eligibility. IAS is qualification to do civil service. So, if you want to a part of an Industry or an entrepreneur, go with IIT. Else you can go with IAS.

After clearing NDA exam, you have to pass SSB test, then only you get into NDA.

For NDA, you need to have subject like physics chemistry in your class 12th. Sorry, try other ways.

Yes, you can give NDA exam if meeting the other eligibility criteria. You are eligible for Army and Naval wing. While class 12th with PCM is required for Air force wing.

Absolutely Right and a great choice. IAS officers are deeply connected to the system and need to be aware of all the laws and regulations. Pursuing LLB is one of the great choice as it will create a foundation for you to excel ahead? Now, the question is you need to decide which stream you want to get you B.Sc Degree. According to me, it would be great if you select a degree related to subjects you will require in clearing UPSC (entrance for IAS). Wish you luck.

The basic beginner's book to practice Quantitative Aptitude for bank exams is RS Agarwal, Arun Sharma, Arihant Publications. You should search online for material, practice mocks and refer class's website for some free study material.