I'm a little confused about baud rate in general. Does it only affect serial communication?
No, as serial communication takes time it can completely corrupt your sketch in theory as communication overhead can cost too much time. So you better use 115200 iso 1200 baud. You can even go higher (230400,345600) with the Arduino but the IDE serial monitor can only handle up to 115200.
Does 50 milliseconds at 9600 bps = 50 milliseconds at 57600 bps
50 millis == 50 millis
But the microdelay between two pulses at different baudrates differ substantially:
9600 baud => 1.000.000 micros / 9600 = 104.16 micros
57600 baud => 1.000.000 micros / 57600 = 17.36 micros