Can I communicate with a STM32 over SWO?
The name of the pin is self explanatory I think. SINGLE WIRE OUTPUT. It is for the debugging purposes, uses very specific transmission and programming methods. 

I do not understand what for. You have plenty other interfaces available. You can use SPI (as my Universal Plus HATS - https://www.diymat.co.uk/product/universal-plus-hat-raspberry-pi/), I2C, U(S)ART, USB, CAN .....