If the USB slots on the back of the motherboard don’t support USB 2.0, can you use USB 2.0 by installing a PCI card with USB 2.0 slots? Or will it be impossible to use USB 2.0 on a motherboard like this?
Hi and Welcome!
that’s why USB 2.0 cards are available 
Please note, that a PCI card will only reach about 16 MBytes/sec (compared to good integrated USB controllers that reach about 30 MBytes/sec).
I strongly recommend cards with NEC chipset which are the most compatible ones. And stick with the USB2.0 drivers provided by the operating system instead of installing drivers from the manufacturer.
Michael