Does Applied Researchers reduce repeat costs?

Yes — once Applied Researchers is Empowered, her "your spells cost [1] [A] less" 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 discount is a total-cost discount applied after all costs are summed (Rule 356.4). So a spell costing [2] with a [Repeat] [2] cost totals 4, and you'd pay 3.

The discount applies once to the combined total — it doesn't reduce each Repeat execution separately — and the "to a minimum of [1]" only caps her Energy discount, so it never prevents the reduction.