Would the gnome Pyromaniac trait ability to cast Produce Flame (not on the Bardic Spell list) count as the fire spell needed to meet the prerequisite for this feat? (Assuming she also has the 5 ranks in Spellcraft)
No. SLAs are not spells.
No. SLAs are not spells.
Good to know. Looks like a 1 level dip into Cleric of Sarenrae (fire and sun) or Fire Elemental Sorcerer is in order.