Can I (mis-)use my USB-to-parallel (printer) cable as UART cable in some way (e.g. sticking some cables in the female parallel output and use them as UART connectors)
In the past the parallel port of a PC was a popular way to allow it to interface with hobby-ist bits of kit that needed a few IO lines, indeed one popular usage was to bit-bang an I2C controller.
Nowadays you have a whole slew of GPIO pins on your RPi that renders the need for such hackery pretty much unnecessary (hell, it even gives you one or possibly two native I2C buses)! I suspect that you could definitely use it to work a printer in the intended manner and you might be able to do some hackery like this (but it very much depends on the driver software) - but to be perfectly honest I can not see a usage case for the latter that can't be done with just the RPi directly or with a bit of interface circuitry attached to it.
<aside>A friend and I, who both worked for a company designing TVs developed a bit-banging IR unit back in the 80's that hung-off a parallel port like that and used 8086 assembler to generate the modulated 38KHz signal to emulate the remote-control protocol of the sets we were designing. This was so that we could test software features that needed new buttons that we had not yet included in the remote-control hardware for the models that needed them...!</aside>
According to electronics.stackexchange.com it is not possible at all:
The UART interface send data serially. It has a TX (transmit) and a RX (receive) pin, and a few optional control lines. On the other hand, parallel interface has 8 data bits and a few additional (different from UART) control lines. Not the same beast at all.
the data lines can generally be used as IO lines providing the host has the software to support this. This can lend itself to a form of serial comms (similar to UART) but it will be totally reliant on dedicated software loops reading the data pins. In other words, it doesn't have the specific hardware chips to inform the host that a new byte has arrived and that byte has no detectable errors and all the other bells and whistles you get with those specific UART chips