Is "istikharah" (guidance-seeking prayer) prescribed in the Quran or not, and how is it performed? And if it is not, then how does one know the answer regarding a certain matter after performing the "istikharah" prayer without reaching any conclusion?

The Istikhara prayer is not to be used for foreseeing the future or knowing the unseen, as this is forbidden and leads to deviation. Knowledge of the unseen belongs to Allah alone. The purpose of the Istikhara prayer is to facilitate good for the servant and distance them from evil. There is no specific answer after Istikhara; rather, the Muslim proceeds with what their heart is inclined towards, relying on Allah, and good will be in it, by Allah's permission.