Non scholar here.... and I love the Greek Myth references....

Helios was a supporter of Apollos, and his Chariot of fire being pulled by Helios in lore.... obviously Helios should be fire/flare/solar themed....

What if Helios was used as many DPS have wanted a BLM to be used as.... to elementally enhance the DPS...

Like Vivi/Steiner dynamic in FF9....

Helios could ideally buff up an ARCHER (Apollo).... by adding elemental burn type damage to his arrows....
Helios could buff up a DRG's Spear....... maybe adding burn damage to his spear
Helios could buff up a MNK's weapons as well.....

So what i am basically saying is... rather than creating an elemental aspect to damage in the game, which unfortunately is missing.... maybe Helios could AOE a buff to all party members to help out the melee dps by adding a "Burn" type element to their attacks that could stack for 30 seconds with each attack

Ability 2 could be used to buff up the mage's INT.... yes an INT buff.. which will help the BLM's raw ability, could increase a SMN's pet ability, could even buff up Helios's own physical damage

Ability 3 could be like shadowflare in a way, creating a red bubble (there isnt a red one yet), that will help increase the tanks physical/magic resistance