If water is unavailable, and seeking or purchasing it would cause the prayer's time to expire, is it more befitting to perform tayammum and pray, or to go and fetch the water even if the prayer's time expires, with clarification on the ruling regarding short and long distances in this matter?

The question includes two issues:

The First Issue: Obtaining water: The accountable person must exert effort to obtain water for every prayer, by asking for it or buying it at a customary price that he does not need. It is not permissible for someone who lacks water to perform tayammum (dry ablution) except after seeking it. Seeking water is only obligatory within a short distance that the person can manage. If the distance is far and difficult to traverse, seeking water is waived, and he may perform tayammum.

The Second Issue: Fear of the prayer time expiring while seeking water: Most scholars hold the view that a person should seek water until he obtains it, even if that leads to the prayer time expiring.

Accordingly, if you prayed with tayammum while able to obtain water – even if after the prayer time had expired – your prayer is invalid and must be repeated according to most scholars. Although we do not issue a fatwa (religious edict) affirming the validity of the prayer in this specific case, there is no blame upon you for not repeating the prayer, because many scholars have permitted acting upon a less preferred opinion after the event has occurred.