A Mexican Mauser dated 1931, is this the small ring Mauser that's desirable to build a sporter? I imagine it's the 1910, are the Mexican national ones as well built as the FN's?

yes.. here's 50 bucks for it!!
jeffe

Mexican-made Mexican Mausers are small ring, intermediate length 98 Mausers, the only such configuration, very desirable IMO for a custom rifle chambered for an intermediate length cartridge. Unfortunately they are a little rough but are made of good quality steel and clean up nicely as long as they aren't badly pitted. FN made Mexicans are regular standard length large ring Mausers, better fit and finish, but not the same animal.