Does SALOME provide some free open source solver?
No, there is no solver which comes with SALOME platform, but there are some solvers which can be used with it transparently. For example Code_Aster (please visit http://www.code-aster.com/). Also there is a site http://www.caelinux.com which provides a special Linux distribution including SALOME, Code_Aster and other free solvers.