The dot-matrix printer I am using is the Epson LX-300+II and it has a USB, SERIAL and PARALLEL port. Is it possible to bypass the epson print commands and send information straight from the arduino to the printer through one of these ports or do I have to use a computer with the printer driver?
don't need a driver (if you use the serial or parallel port). There is a clue in the specs since it lists a couple of different character sets. In the old days (before Windows) the printer's user manual would com with an ASCII chart
and a list of "escape codes" for switching-on bold, underline, using graphics etc.
Since all that stuff is now normally taken care of by the driver, and basically hidden from the user, and no longer needed he programmer, it might be hard to find. The good news is that Epson standardized the codes to work on most of their printers. (Sending ASCII text is simple, but I don't remember how to "directly" print graphics.)