Hello!

Summoning Jutsu Level increases its experience every time you unlock or activate a Hexagon Tile, each Hexagon gives 1 exp for your progress (refer to the image below).

And for the Activation of Summon Mystery Skill, you need to have an item called Mystery Gem that you can purchase from the Group Shop. Each summons has its own required number of Mystery Gem, while some others need Breakthrough Stones for them to have more Skill Effect (refer to the image below).

Hope it helps you, thank you.