Historically, solvents were avoided because the pacing material would swell, changing the pore size, or otherwise damaging the media. They have become more robust lately, so you can add a little solvent, but many people tend to avoid that, out of old prejudices.
The mobile phase is typically a pH buffer, and fixed ionic salt concentration. Whatever's needed to keep the analyte in the correct 3-D structure for proper analysis. This is usually clear, when you consider analytes, they are either large biomolecules , or synthetic polymers.