In light of Qur'an, and Hadith, I would like to know what is the ruling regarding following scenario:When attending congregation prayer one finds that there is no place in the available row, and one has to finish the prayer standing alone. Is the prayer of such an individual valid? If not, what are the requirements to make it valid?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Anyone who does not find a place in the row for prayers and there is no one to stand with him in a new row, he may perform the prayer alone behind the rows; his prayer then is correct and valid, this is the preponderant opinion of the Muslim scholars.
Allah Says (interpretation of meaning): {Allâh burdens not a person beyond his scope. ……….}[2:286] Allah also Says (interpretation of meaning): {So keep your duty to Allâh and fear Him as much as you can; …………}[64:16].
The meaning of the Hadith narrated in al-Musnad that the Prophet ordered the one who performed prayer alone behind the rows to repeat his prayer, is specific to the person who intentionally stands alone behind the rows. Some scholars believe that if he is alone behind the rows he may pull a person back from the row, in front of him. But according to the prevailing opinion one should avoid doing so since this may cause a gap in the row, which is not permitted in Shariah. The Prophet said: "Straighten your rows and put your shoulders close to each other and be gentle with each other and fill in the gaps for the Satan passes through what is between you like small sheep [are able to pass through gaps]." This is related by Ahmad and at-Tabarani with a chain that has no fault in it.
Also, by pulling him back he disturbs the praying people and transfers that person from a higher position to a lower position, i.e. from the forward row to a rear one.
Allah knows best.