It could be one of many; 10, 12, 14, 15 to name a few.
You can get a historical letter from S&W for 50 USD.
Model 10
The "J" frame is the Smith & Wesson small frame revolver such as the model 36 .38 special. The smallest frame, as in the model 36 Chief's Special.
What model .38?
38 special is only a revolver caliber. that's like saying a 44 magnum revolver or a 500 special revolver. a revolver is a revolver
Impossible to answer without a serial number; 10-500 USD
100-425 USD
You will have to get it lettered by S&W to find out.
No way to tell model from jus the serial number.
It depends on what you mean. A .38 revolver may be a .38 special, but there are other types of .38 besides just the special round.
100-500 USD or so
Need the sn to answer