Why does this "square wave" have what seems to be a charging action on it's leading edge?
This line:

DDRC ^= (1&lt;&lt;DDC1);


is actually inverting the direction of the PC1 pin at every iteration of the while loop. This places the PC1 pin in output mode and probably LOW state during one half-cycle and then in Hi-Z mode during the next. The impedance of the PC1 pin is then 10k-100kΩ, so this acts as a very poor RC circuit with the parasitic capacitance of the breadboard and PCB.

Your square wave is an RC circuit for half a cycle then a driven LOW for the other half, hence the waveform you are seeing.