As a side note, intermetallic compounds can happen in any process; soldering, brazing, welding, casting, etc. Most are bad because they are brittle and are often crack nucleation sites, however some compounds can have various strengthening effects, though not typically in solders.

Eutectic alloys are also notable because they often have the lowest melting point (unless there are multiple eutectic points). The liquid/solid together explanation was kind of an unclear explanation in my opinion. What the author meant is that a eutectic alloy does not have a range of temperatures where liquid and solid can coexist in a stable state (the general case for multicomponent materials), upon reaching the eutectic temperature, the solid immediately melts into liquid.