I'm making a Life Oracle for an upcoming campaign, who has the "Merciful" third-party Curse, but scaled up a little more (basically unable to directly take a life that is not undead). He'll be almost exclusively a buffing/healing character, with a lot of focus on Channel Energy, so I'm looking specifically at Fateful Channel. Would a Life Oracle that (with backstory provided) worships Pharasma be able to take this feat, or do you have to get your powers directly from that deity (à la Cleric) in order to gain feats with this type or prereq?
You don't have to be a Cleric to worship (most) deities! Most characters in the Golarion setting worship one or more gods, and most if not all cults are composed primarily of worshippers other than mortal humanoids of the Cleric class. The prerequiste line for Fateful Channel (as well as most other deity-specific feats, traits, and equipment) merely requires that you be a worshipper of the deity, not that you be a Cleric of that god or goddess.
That said, many deity-specific feats and traits interact with the channel energy class feature or other features of the Cleric class and have prerequisites reflecting this. Fateful Channel does possess such a prerequisite, but you can certainly meet that with the Oracle's channeling ability instead.