The Royale is a trim level and not an actual Oldsmobile model. See Sources and Related links below to lookup your vehicle by make, model and year. Usually the Royale trim level takes the same wiper blade sizes as the base model. It will be listed separately if not.
The windshield washer pump is inside the wiper motor and serviced separately.
The windshield wiper fuse is located in cabin fuse box in slot 16. To find the cabin fuse box remove plastic panel on the underside of the dashboard.
Was there a 1984 Oldsmobile Cutlass Calais? I see them listed at 1988-1991. Assuming that you mean "wiper blade" (blade and frame) which are replaced often rather than "wiper arm" (piece from the spindle at the hood to the wiper blade) which are rarely ever replaced, ALL 1988-1991 Oldsmobile Cutlass Calais' have 3/16" Side Lock wiper arm attachments. See Sources and Related Links below.
On a 1984 Pontiac Fiero, the wiper motor is located under the windshield, mounted on the driver's side. It can be accessed by removing the plastic cowl cover that runs along the base of the windshield. Once the cowl is removed, you'll find the wiper motor attached to the wiper linkage. Make sure to disconnect the battery before attempting any repairs for safety.
The motor which controls both windshield wipers is located under the metal cowling at the base of the windshield.
Looking at the engine, in front of the car, there is a fuse box behind the battery. Open up the black cover and inside is the fuse for the wipers.
Night of the Blade was created in 1984.
The 1984 Oldsmobile Cutlass Supreme takes 18" replacement windshield wiper blades on both sides front. Note, when buying wipers be sure to always lookup your vehicle make, model and year in the application guide book at the store, or now-a-days you can Google 'lookup wiper size'. You want to look this up because correct wiper fit is more than correct length, it's also proper attachment. Not all attachments fit all arms. Using the application guide or looking up wiper size online will avoid headaches of buying the right lengths with the wrong attachments.
First check fuses, relays to wiper motor. Then check power to wiper motor. Then check linkage to wiper motor.
Yes
check the bottom of the windshield on the driver side. or up at the top
on My 1984 LeSabre, I found that there is a tab near where the wiper arm mounts to the pivot. If you bent the wiper arm back and pull the tab out with a pliers your can then remove the wiper arm. After you put the new one one you have push the tab back in. It has to go far enough in for the spring to be able to pull the wiper against the window.