Your question brings together a number of different points that it is difficult to address with a single answer. In general, we would say the following:
1. It is well known that Allah encourages us in the Qur’ân to vie with one another in doing good deeds Allah says: “So vie with one another in good works” [Sûrah al-Baqarah: 148, Sûrah al-Mâ’idah: 48]
Allah says: “And vie one with another for forgiveness from your Lord, and for a paradise as wide as are the heavens and the earth, prepared for those who ward off (evil)” [Sûrah Al `Imrân: 133]
Allah also says: “And the foremost in the race, the foremost in the race: those are they who will be brought nigh in gardens of delight.” [Sûrah al-Wâqi`ah: 10-12]
2. This competitiveness does not necessitate negative consequences upon others, since it is not a win or lose competition. Each Muslim strives to increase his good and go forward without this increase bringing about any decrease for anyone else.
This is why the Prophet (peace be upon him) prohibited envy, wishing for another to lose the blessings that he possesses. However, he permitted a person to desire to enjoy the same blessings as well.
3. We must be ever vigilant against Satan so that our intentions do not turn sour in these endeavors. A Muslim seeks knowledge, not with the purpose of being more knowledgeable than some other person, but rather to worship Allah with proper insight and to carry out the duty of acquiring knowledge on behalf of the Muslim community.
As Muslims, we discuss and debate not so that we will be the winner of the argument, but so that we and everyone else can arrive at the truth. We engages in righteous deeds not so that others can applaud us, but to increase our account of virtues.
We enjoin virtue and prohibit vice not so that we can order others around, but so that we can fulfill our duty to the people and convey Allah’s Message.
And Allah is the giver of success.