Line impedance in 4 layer PCB
Assuming Signal Layer 1 is the ground plane, then yes, the distance H is the distance between Signal Top and Signal Layer 1.

The tool you are using is correct provided you are not using it for differential signals. If you are using differential signalling then you need the differential microstrip impedance calculator. If you want to calculate the impedance of a track on an internal layer, then you use the stripline impedance calculator.