I believe the rifle in the pic is a 1903, not a 1903A3. The A3 had a peep sight, the 1903 had the open sights.
C3, IIRC, the Pedersen device used a standard .32 ACP. some military experimental ammo was made by the arsenals with a different headstamp, but I believe it was .32 ACP.
I might be mistaken, but that's what I remember from reading in American Rifleman many years ago.