Are binary molecular compounds generally composed of a metal and a nonmetal?
No - generally nonmetals
The words "molecular compound" implies the compound is held together by covalent bonds (chemical bonds.....sharing of electrons).
Ionic compounds, on the other hand, are composed of ions that interact with each other through +/- interactions (something analogous to the N end of a magnet "sticking" to the S end of a magnet).
Binary Molecular Compounds are covalently bonded compounds that consist of 2 atoms, and these atoms are usually (almost always) nonmetals (think upper right side of periodic table, and H).
Things like Water
Binary Ionic Compounds would be things like NaCl,