How to measure quantities at standard state when this state is a hypothetical one?
The standard states are limiting states. In these limits you can write the chemical potential of the component as 

$\mu = \mu^\circ+RT\log(x)$

where $x$ is a measure of the concentration of solute (for Henry's law, where the standard state is a hypothetical state related to the behavior as $x \rightarrow  0$) or solvent (for Raoult's law, where the standard state is approached as $x \rightarrow  1$). In other words, in the limiting states the activity goes to 1. The meaning of $\mu^\circ$ depends on the limiting law (hypothetical with properties of an infinitely dilute solution or pure solvent).

A standard state can be hypothetical (as may happen when Henry's law is invoked), but it can also be real (as in Raoult's law, for a pure solvent). It is a state in which the sample behaves ideally as defined by the above equation, in the limit of infinite dilution or of a pure solvent. This limiting behavior provides a convenient and predictable reference, like setting the potential energy to zero when particles are separated by an infinite distance. In the case of Raoult's law, the standard state is the (not particularly mysterious) pure substance. In the case of Henry's law, the reference state is found by extrapolating behaviour at infinite dilution to the standard concentration (1 molal or 1 M, conventionally). This may be a hypothetical state.

Using reference standard states (at 1 bar of course) can simplify combining or comparing data for different substances or conditions. Of course when considering real solutions, activities may diverge from concentrations and activity coefficients deviate from unity. 

For a mixture of substances, for each component you can describe individual thermodynamic properties relative to the ideal standard states. By ideal it is also meant that individual solutes do not interact.