av8r64 - I believe you have the target variation of the .38 Military and Police Model of 1905, 4th Change. Many of the basic fixed-sight M&Ps were manufactured (production continued from about 1915 to 1942), but the target models, with square butt frame and adjustable target sights, were somewhat rare and are therefore more valuable. As you noted, yours is unfortunately missing the rear sight and also the thumb latch (I'm also not sure if those are the original grips - they should have a raised diamond around the screw holes). I don't know about the availability of parts.
It's not possible to pin down the actual year of manufacture because SCSW just lists the 1915 (at SN 241704) to 1942 (SN 1000000) range with no further information. You can get an idea by interpolating between those two numbers, but it will only be an approximation.