1. There’s a print shop called Copy General that’s centrally located and reasonably priced.
2. Local hotels all have business centers, I have used the Courtyard‘s on Voznesensky per., the Marriott Grand‘s on Tverskaya (also for DHL), and the Mercure near Stariy Arbat. I recently stopped by the Mercure at the crack of dawn and their lobby staff printed documents for me before a 6AM flight. Otherwise, hotels won’t generally print 24/7. Like in any city, go for the mid-range business hotels.