Adolph Schild 5203, or 5206 with day removed. Can be found NOS in Zeno-Watch Explorer with day and date removed, which would actually make theirs 5202s. But who's gonna argue about a moment that hasn't been made since the mid 70s? They're all the same ébauche anyway.
And for the record, anyone who doesn't like their crappy old A2xx, 4xx, 5xx, 6xx, 7xx, 10xx, 11xx, 15xx, 20xx, 21xx, 22xx, 30xx, 31xx, 40xx, 41xx & 65xx Aegler/RWC movements, I'll be glad to pay postage to get them out of your hair, in any condition, just to help put you at ease.
No. ETA is not a Rolex movement. Rolex Watch Co was not a Rolex movement either, until recent acquisition and consolidation. RWC was the renamed Aegler, which made movements for Rolex and Gruen until Wilsdorf invested a significant amount of money in them to convince them to produce movements exclusively for Rolex, hence the name change.
Cases have not always been Rolex either. A L Dennison was an early supplier, and Borgel was the producer of water resistant cases prior to theirs being used in 1922 by Rolex. The first Oyster cases were made in 1926 by C R Spillman SA.