[Mages] can level by solely casting spells, but it is not very efficient. Unlinke studying spells, which allows a mage to gain a lot more experience, making it far more likely to level up using that method. 
According to Pisces, there are seven, or eight tiers. Apparently there is the speculation of the ninth tier , but no mage has ever cast or discovered a spell of such magic.
There are currently 6 known archmages, "the rarest of spellcasters". "One in the Human lands to the north. Two more in other continents. But at least three have homes in Wistram, the Isle of Mages.” However, none can be found in Izril.
“You fly through the air like the greatest of [Archmages] I am told. And you build buildings into the sky.” This implies that [Fly] is a highly difficult spell, perhaps belonging to the 7th or an even higher Tier .
“Long distance teleportations usually require a spell circle and time. If a person teleports instantly, it means that they haven't travelled very far, and are going to appear at a prearranged destination, making it rather easy to locate them.