Bingo!
1. Whenever you need me. - "All you do is call me, and I'll be around." He's a summoned creature, so it seemed like it'd fit.
2. I want to say I came first. - This is more a dummy clue than anything; it's more a reference to other legends regarding Ifrit/Efreet/Afreet.
3. Great sage, this is the only time you'll be able to evoke my help THIS directly. - FFIII clue. Was named Heatran, and both Sages and Evokers had a 50% chance of him healing the party; all other instances of Ifrit showing up in the series involve causing much pain to the enemy.
4. I'm not the wind. Far from it, actually. - FFIV's Ifrit was named Jinn in the SNES release. So was the elemental of Wind in Secret of Mana.
5. So The Library has a job for me? - FFV clue. He was there to burn the books possessed by demons.
6. With me, you'll know how to burn things real good!... I'm drained, though. - FFVI clue. He teaches Fire, Fira, and Drain, not to mention he's completely drained with Shiva when you find him.
Unused clues!
7. I come after Birth. - FFVII clue. He appears right after Jenova-BIRTH.
8. It'll be a Mad Rush to kill every enemy that crosses our path - FFVIII clue. Mad Rush is a skill unique to Ifrit without using items, right?
9. With my favorite piece of Jewelery, you'd have thought I was born in November - FFIX clue. Topaz, enough said.
10. There's a kid in my town that says he wants to be a Blitzball. What? - FFX clue. I don't think I really need to say any more.
11. These clues aren't all just single instances of me. - If I got this far without people getting it, it was the point to get people to think a little more outside the box.
Your move, RC.