Wiring – Maytag Dryer wiring issue

Assuming you are asking about US residential biphase 240 volt wiring (or equivelant), then there is nothing wrong with reversing the black and red wires.

The schematic image you've attached is difficult to see, so I can't say for sure. Based on the wiring, I would say that the B terminal would work as C.

Since I'm not there and can't test things, I have to make some assumptions. Based on the wiring, it looks like the one cable goes to the thermostat and another goes to the outdoor air conditioning unit. Since the red wire from the A/C cable is grouped in on the Y terminal, and the white wire from the A/C cable is on the B terminal. One can reason that the B terminal should be connected to one side of the transformer coil, while R is connected to the other.

You can test this theory by setting a multimeter (or voltmeter) to AC volts, and testing between the R and B terminals. You should read ~24 volts.

You can either connect both the white wire that's already on the B terminal, and the new C wire to the screw terminal. Or you can connect the white wire and your new wire together with a spare bit of wire, using a twist-on wire connector. Then connect the other end of the spare bit of wire under the B terminal screw.