Yes to the first, no to the second. Both consoles will run unsigned executable files, but you may need to reverse engineer your own solution for getting those

Yes to the first, no to the second. Both consoles will run unsigned executable files, but you may need to reverse engineer your own solution for getting those files to run in a user-friendly manner. There is software created for earlier PS and Xbox consoles (for example, Kodi on the Xbox, Linux on the PS). It simply took a few years for third parties to understand the hardware well enough to write their own code to run on the consoles without using the console makers' IP.