(Sorry this was incredibly delayed Vipin I remembered I hadn't finished it when I saw your post about justice.)
Well Vipin you're addressing a deep doctrinal issue here which even among protestant denominations there is not a complete consensus. Martin Luther as one of the first protestant theologians, of course, did not get everything right, he did get a few things incontrovertibly correct the most important of which was his rallying cry of "sola Scriptura". As you confront doctrinal issues like this you will find that nearly all of the established denominations have slightly different to profoundly different interpretations on the fundamental doctrines of the Bible, which is odd but given human nature, understandable.
Vipin wrote:We received righteousness as a gift and outside of ourselves. Then the Bible demands us to walk in the righteousness we received. How is it possible? So there is some sort of infusion or impartation happening. Right?
Well, this is a bit difficult Vipin as I don't know what base you're coming from Catholic or Protestant, I am well familiar with both. Unfortunately, if you are coming from a Catholic base then just about nothing I say from this point on will be in line with their teachings. When it comes to Biblical Doctrine Martin Luther did indeed invalidate the Catholic church's fundamental teaching of the nature of salvation and the process of a believer's sanctification (living righteously) on the basis of Biblical authority.
You seem to be hung up on the notion of righteousness and I'm not sure how exactly you are using that. There is the righteousness that is yours at salvation, the moment that Christ's sacrifice on the cross becomes applicable to you, that righteousness is how God sees you, it makes you acceptable to be in his presence for all of your sins are at that moment forgiven, actually, your soul is wiped clean, as is said: "washed in the blood of the Lamb".
Then there is the righteousness of your behavior which will increase over time as you live your life in accordance with the precepts of discipleship, this is the one I think you are asking about. It is important to know the difference.
Let me see if I can help by giving you a brief synopsis of what I am convinced the Bible actually teaches about salvation.
First of all, all have sinned and fall short of the glory of God, Romans 3:23. This is but one verse that speaks to the depravity (sinful nature) of man. The doctrine of man's depravity is well established and universally accepted throughout Christendom.
There is only one path to salvation and that is through Jesus Christ, " Jesus said to him, “I am the way, and the truth, and the life; no one comes to the Father but through Me." John 14:6
Salvation is a gift from God there is nothing, absolutely nothing that a human can do to earn salvation. "For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; not as a result of works, so that no one may boast. Ephesians 2:8-9 We'll come back to this passage with the addition of verse 10 because I suspect it speaks directly to your issue but first.
How does someone become a Christian in the first place?
There is only one way, a conscious and sincere appeal to Jesus Christ to become the Lord of your life, and only by doing that does He become your Savior.
You will often hear evangelists quote Romans 10:9 "...if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved;" This is commonly interpreted to mean if you believe that Jesus Christ was who the Bible says he was and you testify to it, you will be saved. That is not the requirement of salvation.
Here is the requirement of salvation...
"Then Jesus said to His disciples, “If anyone wishes to come after Me, he must deny himself, and take up his cross and follow Me." Mathew 16:24
I'm saying all this Vipin because it is my conviction that attempting to live as a disciple of Christ without this level of understanding and commitment is impossible. To walk in the righteousness of God as described in the Bible is to be a Christian in thought, word, and deed, and to do so with as much consistency as possible. This is a daunting task. The way to do that is completely outlined in the Bible and begins with a commitment to reading the Word and considering its meaning on a daily basis. It is also of considerable help to find a fellowship of other Christians with a similar commitment.
However, the good news is if you have a good Biblical understanding of what it takes to be a Christian then the Bible also gives you all the tools needed to do so you just need to read it.
You should know that I do not agree that there actually is any such thing as the God of the Bible. I did at one time and was actually an evangelical minister for a number of years. I have profound respect for people who become true disciples of the Christ described in the Bible and none whatsoever for the vast majority of hypocrites that claim to be. The life of a true disciple can be a very rewarding and fulfilling experience though and I wish you luck should you choose to pursue it.