It is best to avoid pins 0 and 1 because these hardware serial pins are handy for debugging using the serial monitor.
You have not told us what Arduino you are using, but it might be best to use one of the software serial solutions (there are a few) so that you may use other pins. Alternatively, if you have a Mega, you may want to use Serial1, Serial2, or Serial3.
It is hardly worthwhile to print out the start and stop bits because they never change. If you want to see start and stop bits, a logic analyzer may be the way to go.
Parity bits have me stumped. They can be seen on a logic analyzer, or they may be computed, but if there is a way to see them in the hardware I do not know what it is.
I suppose you could hack the software serial library for start bits, stop bits, and parity bits if you REALLY need it.