The Hearthfire mannequins dupe generic armor - I too have duped Ancient Falmer Armor, but could not dupe unique items like Gilded Wristguards and the Jagged Crown. Downside is that these mannequins will destroy any self-made enchantments and smithing boosts on generic armor, so don't place any such apparel on them for display (unique relics / apparel like say, Yngol's Helm are unaffected).
Haven't actually tried duping on vanilla-house mannequins post-patch.
I've never had problems with any plaques or racks in general, just specific items. Deathbrand's twin scimitars are painfully buggy for decoration, for example.
One problem people might be running into with weapon racks is that they will sometimes not work if other self-placed items are touching them or are close enough to cause a glitch; move or pick up any items around the plaques and see if that helps.
Simple questions deserve long-winded answers that no one will bother to read.