Welcome to the forum.

I just picked up a Model 30-1 off lay-a-way. It is the round butt version of your 31-1, which should have a square butt.

Yes, you can shoot 32 S&W and 32 S&W Long in a gun chambered for 32 S&W Long.

It is the same as shooting 38 S&W Special in a gun chambered for 357 Magnum; or 44 S&W Special in a 44 Magnum.

You will find that the shorter cartridges leave carbon/powder/lubricant residue in the portion of the chambers normally occupied by the longer cartridge case. After a long shooting session, the chambers may need to be cleaned before they will easily accept the longer cartridge case. Other than that minor issue, fire away.