why does a current carrying conductor sets up a magnetic field?

The electric field and the magnetic field are tightly interlinked, in two senses.

First, changes in either of these fields can cause ("induce") changes in the other, according to Maxwell's equations.

The magnetic field generated by a steady current, is described by the Biot-Savart law. This is a consequence of Ampere's law, one of the four Maxwell's equations that describe electricity and magnetism. The magnetic field lines generated by a current carrying wire form concentric circles around the wire. The direction of the magnetic field of the loops is determined by the right hand grip rule. The strength of the magnetic field decreases with distance from the wire.

Second, according to Einstein's theory of special relativity, a magnetic force in one inertial frame of reference may be an electric force in another, or vice-versa.

Yes there is a electric and magnetic field around the current carrying conductor. Air can also conduct (very week conductivity) electricity. Because, an ideal insulator must have resistance of infinity, but practically nothing as infinite resistance. so there is leakage of electric filed around the conductor. The voltage is gradually decreased around the conductor and comes to zero. Thats all depends on the voltage in the conductor.

Good question. If you think about a stationary electron, it has a static electric field. If you place the charge in uniform motion (constant speed) the electric field's spatial distribution changes over time (If you sit at any point in space, you will see the field value chage as the charge moves - it will increase as the charge moves towards you and decrease as it moves away). But you will also measure a magnetic field. One way to look at why the magentic field is present is that the Lorentz transformation from the charge's at-rest frame of reference to your frame of reference (where the charge moves) requires some of the potential energy in the electric field to give rise to the magnetic field.

Another way of looking at it is if the electric field is varying in time, then Maxwell's equations requires that there be a spatially and temporally varying magnetic field.

its can capturization of the ac current then that conductor can purify the pure voltage , i.e to supplying the power to system i.e it make work like filtering

it is due to electromagnetic induction