Right. The current will change in one direction (decreasing, passing through zero and increasing) as long as there is voltage across the inductance of one polarity. As soon as the voltage reverses polarity, the current stops increasing in that direction and starts to decrease, pass through zero and increases in the other direction (all change in one direction). The formula that relates inductive voltage to current is V=L*(di/dt) with V in volts, L in henries and di/dt in amperes per second.
Are you saying the same voltage is applied to both wires, but of opposite polarity? If so, their currents would be equal but opposite. No new frequencies.
No. Everything except power occurs at the same fundamental frequency.