Correct

Yes, a UEL is more general and must include the constitutive update (UMAT) within it to form the element matrices required as input back to Abaqus (AMATRX, RHS, etc.) at the end of the UEL call.  To my knowledge, there isn't a "nice" reference apart from what is in the Abaqus manual in regard to constructing the code, but its not terribly hard to do for standard finite elements (post-processing the results, however, is a different story).  I may be able to dig up a copy of 4 node quad element UEL that I did for a nonlinear FE class project if you're interested in looking at that.

Jason