flipdot | Hard- and software to control a LAWO flip-dot display | Animation library

I'm under the impression the pyserial package may allow me to send the same bytes through the same pin.

pyserial will let you send data out a serial interface. It has nothing to do with Arduino. If all you want is for this serial data to go to your display then there's no need for Arduino at all. Just connect your serial lines to the display and send serial data directly from the PC.

I also need to figure out how to replicate the setup and loop functions

That's very simple. Write the code that you want to run once first, and then put the code that you want run in an infinite loop into an infinite loop. while(1) works well to create an infinite loop. There's nothing special about setup or loop functions on Arduino. They're just regular functions that get called from the main function. setup gets called once and then loop gets called in an infinite loop.

It really isn't clear why you think you need to involve an Arduino here. If it is simply that you don't know how to connect things to a PC then perhaps a Raspberry Pi would be a better choice as it can both run python and has GPIO pins that you can connect things to. A second option would be to load firmata on the Arduino and use pyFirmata from python to control that. You can google both of those terms, there are lots of tutorials on how to do that.

I think you have some fundamental misunderstandings about what an Arduino does. Perhaps it would do you some good to spend some time away from this project learning some of the basics and then return to this once you have some experience and a little bit of understanding about what all of these things mean.

The larger question is why do you want to involve python? Is there a reason it needs to be controlled from a PC? Or is it just that you don't want to learn a new language? Those are two very different issues that would promt me to give you very different responses. If you need to be able to control the display from a PC then just do that and use your Arduino for something else later.