What is the ruling on choosing airlines that offer a points system to benefit from it in reducing the price of future tickets, and what is the ruling on using these points to pay a small part of the ticket price?

There is no harm in using airline points to reduce the ticket price, because it falls under selling the ticket for less than its customary price, which is permissible as long as it is with the consent of both parties. The customer may also receive a free ticket, and this is permissible because it is a gift from the seller to the buyer. It is stipulated that the original ticket price should not be higher than usual because of these benefits. Sheikh Ibn Uthaymeen was asked about discount cards and he answered with permissibility, stating that the rule is that if a contract involves a person either being safe or gaining, then there is no harm in it. However, if it involves either gaining or losing, then it is not permissible.