The below might resolve the OP's question about Abilities interacting:
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1. Upkeep
Refer to text “if the order in which multiple effects would resolve would affect the outcome, then the affected model’s owning player determines the order in which they are resolved”.
Start with effect Burning +1: this model suffers +1 damage, equal to Burning Condition value,
Interrupt the Burning Condition resolution with Purifying Fire and heal damage instead
- Fire Gamin now refers to Saracenar’s Plight but has not received any damage. Remove Burning Condition.
- Golem now does not end the Burning Condition due to Forged in Fire and ignores the second part cause it didn’t suffer damage anyway (Rail Golem resolved).
The Gamin and Golem would need to be in range of the Aura but this seems like a logical resolution order for the owning player. All three are Abilities and they are all interacting with the Burning Condition during Upkeep.