The cutoff info above is reversed. "ON" allows ammo to feed from the magazine (think of turning "ON" the magazine); "OFF" is for single loading. The idea was not so much about saving ammunition in general, but in keeping the magazine in reserve for an emergency, like a cavalry charge (1903, remember, and the cutoff idea was carried over from the 1892 Krag).
The A1 stock business is more complex. In 1929, the army decided to replace the M1903 straight grip stock with a pistol grip stock, called the "C" stock. But those were times of really tight budgets, so the orders were that the new stocks would not be used until all the older "S" stocks were used up. Since the arsenals, Springfield and Rock Island, had thousands of the old stocks in store, that effectively meant never. But the M1903A1 (the designation for the rifle when it had the pistol grip stock) was the "official" rifle, so when orders were received from outside the army, the rifles shipped had the "C" stock. That included NM rifles sold through the DCM as well as sales to the Coast Guard and some other governmental organizations.
In 1940, after Roosevelt ordered 1.1 million Model 1917 rifles from the war reserve sent to England, and M1 rifle production was very slow, the army contracted with Remington to make the M1903A1 rifle. But the wood blanks available were not large enough for the full pistol grip, so the army allowed Remington to use what was on hand and make the pistol grip as large as they could. Hence the "scant" stock.