My guess is that happens because your hardware clock is broken, which you saw from the error messages when you tried to run the hwclock command, because when setting the time manually in the GUI it tries to set the hardware clock directly. I think the GUI effectively tries to do both “date --set” and “hwclock --systohc” and it needs both of those to work.
The command “sudo hwclock” should show the date and time and not any error messages.
On the bright side, this could mean you have only one hardware issue, the clock, and that you wifi problem is just a consequence of that.
Anyway, I think your best course of action is to contact Purism support by email and explain this to them, probably the output of the “sudo hwclock” command you get will be enough for them to conclude that you have a hardware issue so they should let you send it back. And they will hopefully add “verify hardware clock” to the list of things they check before shipping a phone.