Depends on solvent properties: Polar organic solvents can solve high amounts of HCl ( like Ethanol, Methanol, THF, Dioxan) In unpolar solvents HCl have low solubility ( like Benzene, Chloroform,...
A Hydrogen atom is one proton, one electron. The ion has lost the 1 electron, but it is still the same element, if that's what you mean. Protons are used to define what the element is.