Wood shold be oiled walnut. The Germans when they built these finished them with linseed oiland then recommended the wood be maintaind with german oil which is basically ballistol, though rubbing with small amounts of BLO
will produce the same result. Ballistol was just easier to issue in the field as it doesn't congeal.
The varnish is definitely not correct.
With respect to details, not much to add that you don;t already know. They were purchased in the 1920's to supplement stocks of M1908's that Brazilcouldn't get from DMW anymore at the time b/c Germany
was busy recovering from WW1 and the punishing conditions of the Versailles treaty.