Gibbs free energy can be expressed as a function of P,T and n but are enthalpy and internal energy also (partially) functions of n?
Yes, you can define chemical potentials as partial molar enthalpies, or partial molar internal energies, or partial molar Helmholz free energies.  (Sorry for my initial confusion on this point ... see also my answer on your other question on this topic, here).

The definitions as partial molar enthalpies and partial molar internal energies are not particularly useful, since they involve working at constant entropy, which is practically impossible, but they are still mathematically valid.  

The definition of chemical potential as partial molar Helmholz free energy at constant temperature and volume may actually have some practical applications, (e,g. perhaps for reactions that evolve gases in closed containers? although I have never come across any.