Well, from what little I can see and what you have told me, you have an Early Wartime (1940-1942)
Commercial HSc. It is not marked for Military of Police use. Generally, it would be classified as a "lunch box special" meaning it was probably stolen from the Mauser factory before a serial number was applied in a workers lunchbox, hence the name. The magazine is from the Peak Wartime era, i.e., 1942 to 1943.
I can see that the finish is badly corroded from the environment it was exposed to at some point. That implies that it has not been very well cared for in the past. The pistol's poor condition, at least externally, will have a severe hit to its value and that includes my next discussion point.
There could be a legal issue here. Recently made firearms are required by law to be serialized. I have heard but not seen documentation that unmarked wartime pistols are grandfathered into an exception to that law. This may only become a problem if you intend to sell it.
Hope all that answers the questions you raised (and some you didn't!). Anything else, let me know ... I'll be right here.