Does Applied Researcher affect repeat costs?

Yes — once she's Empowered, Applied Researchers' discount applies to Repeat costs too.

Repeat is an optional additional cost that gets added to the spell's total cost during finalization (Rule 356.2), and her "your spells cost [1] [A] less" is a total-cost discount applied after all costs are summed (Rule 356.4). So a spell that costs [2] plus a [Repeat] [2] cost totals 4, and you'd pay 3 (FAQ #11935). The discount applies once to the combined total — it does not reduce each Repeat execution separately — and the "minimum of [1]" only caps her Energy discount, never prevents it.