Are acids or bases aqueous always?

No, you can measure a pH in an organic solvent as well, not sure what it means though. pH is defined as the log of inverse H+ concentration. read more

Acids and bases can exist in any phase, but reactions are most likely found in a liquids or in an aqueous intermediate. This is because liquid/gases are great for kinetic opertunitity for reacting and H+ protons or electrons (in lewis acids/bases) are easier in a kinetically volatile phase like water. read more

As usually used acids are aqueous solutions; so HCl(aq). The water is needed to form H3O+ which gives the typically acidic properties. HCl(aq) actually contains very little HCl as it has been converted to H3O+ and Cl-. read more