Can a case be filed against the army personnels in a Court?

You can only file a case against an army personnel, in a civil court in situations when there is special permission from the Central Government. However, the armed forces, under their own rules and regulations, have their own courts to try their officers (for offences specified under their own rules and regulations). These courts are called the Armed Force Tribunal.

What will happen if a public servant does a favour, but not through any specific action of mine? Will this be considered as corruption?

You can still be punished if you took the money and made the person who bribed you, believe that you were responsible for the favour. For example, you take Rs. 20,000 from Ravi after making him believe that he got the job with the Forest Department because of your connections with the head of the Forest Department. Even if you did not actually have any connections with the head of the Forest Department, you will still be breaking this law.