Does it have the extractor at 7 o'clock or 6 o'clock? Are there slotted screw heads on the big screws on both sides of the action? The serial number might also help. although there are no records as such a rough time line may be able to be established. It is probably a standard Model 44 but we can't be sure without seeing a picture.

I will take a guess that your Stevens was made between 1898 and 1903,  they quit chambering for the 3240 when the 44 1/2 came out in 1903.  Ledball

The usual recommendation for the 44 in .32-40 is black powder or black powder equivalent loads and lead bullets. Stay on the low end with any load. These actions are marginal for the .32-40. They came out with the 44 1/2 action for a reason and when the 44 1/2 was dropped they quit offering any center fire in the 44 action. The tried the .22 Hornet in the Walnut Hill for a short time but dropped it because the actions loosened up quickly.

As far as I know, yes. My 32/40, 7 o'clock extractor with plain screws has the extra lock up. As does the 38/55.

Frank