Is completing the prayer while traveling a sin for violating the dispensation and Sunnah, or is it like fasting while traveling, where there is no sin? Is it impermissible to perform supererogatory prayers (Nawafil) and regular Sunnah prayers along with shortening the obligatory prayer, especially the rak'ahs for building a house in Paradise?

Shortening the four-rak'ah prayers is a concession (rukhsah (definition)), and whoever completes them, their prayers are valid. Breaking the fast during travel is better if fasting is difficult for the traveler; otherwise, fasting is better. Performing the supererogatory (ratibah) prayers during travel is preferable, and not performing them does not entail losing their reward if their omission is due to travel.