Is there any dependency between kingdom power level (number of stars) and Traitstones coming in Explore? In other words, will I gain Arcane and Celestial Traitstones more often in a high-leveled kingdom?
No, kingdom power level doesnt increase the drop rate of Arcanes in Explore, the drop rate is static. The chances of getting an Arcane from an explore is similar for new, mid and endgame players.
Seconding what @Eika said. Anything that can be leveled (kingdoms, hero, troops, whatever) has no effect at all on the traitstones drop rate.