So in one of the last episodes, Gowther reads the power levels of Diane and King and they increased. Why did they increase? I think the former fairy king and giant king wanted to make them stronger sending them to the past, but the "challenge" they passed there was one not to kill her sister's lover (King) and the other not to betray her race (Diane), but I dont see how this had to do with increasing their power levels, does it?
They gained knowledge and maturity from their trip to the past, which is counted when numbering power levels.
Around chapter 106, we learn from Hawk's use of Balor's Eye that power levels are made up of three numerical components : Magic, which determines the magical proficiency and raw firepower, Strength, which accounts for physical power, and Will which is more abstract, but basically accounts for the individual's fighting spirit and / or maturity as a fighter.
Since King and Diane faced life-changing events in their trip to the past, they can reasonably be considered to have gained a lot of willpower, thus increasing their Will. They also have peered into Gloxinia and Dolor's memories, who use the same magics as them ; they have learned how to use their magic more efficiently.
It must also be noted that King's wings begin growing at this point. In Chapter 218, pages 6-8, this is noted to improve his link with the Sacred Tree and allows him to use the full power of his sacred treasure, Chastiefol. Fairies gain a noticeably huge amount of power when growing their wings ; for example, Elaine went from 2 830 to 21 050.