Laptop battery and adapter voltage ratings
The adapter does not connect to the laptop's battery directly, there is always a charging control circuit in between. In laptops this usually is a switching type charging circuit to avoid excessive power (heat) dissipation.

If the power adapter delivered 14.8 V then it would be difficult to impossible to fully charge the battery as there would be no "voltage headroom" left for the charging circuit.

The choice for 19.5 V instead of 24 V might be historical and practical. 19.5 V did the job and maybe 24 V might require components rated for a higher voltage.

The input rating of the power adapter is just that a rating which means that the current will not exceed the rated 1.6 A. Usually this maximum current is only reached when you plug in the adapter into the mains. During normal operation the current will be much less. How much will depend on how much power is required from the 19.5 V output.

If the adapter would actually continuously consume 1.6 A then it would get extremely hot as it would need to dissipate a lot of power. So no, you will not be paying a bill for 1.6 A.