Re: H&R .32 top break
Assuming your gun is safe to fire (barrel isn't blocked or dented, no cracks in cylinder walls, etc.) it should be able to handle modern low pressure .32 S&W shorts and depending upon the model (which I can't tell from the serial number) probably .32 S&W Longs also. It was made close to the 1930's - 1935 time period if it is what I think it is. If not, then it was made a little earlier.
Jim Hauff ~ H&R Collector In Memory of Bill Goforth and Jim Ritchie