Current on each winding of a solenoid and wire selection
The 'volts per turn' of a winding depends on the flux linkage. In the case of a high permeability core like iron or ferrite, all turns whether large or small share essentially the same flux, so each turn has the same voltage generated across it when the flux changes.

You specifically mention air-core solenoids in your question. Here, outer turns of a multi-layer solenoid will enclose more flux, so will have a higher volts per turn due to flux changes.

Whether all turns run at the same current is a matter for how you've connected them. If all are in series, then they all share the same current. If several turns are in parallel, then they may share current unequally.

If you are simply using the solenoid to generate a static magnetic field, and have wound it from a long length of wire, then once the transients have died away, the longer outer turns will drop more DC voltage across them, as they have a higher resistance than the smaller inner turns.