No faq at all on motherboard site, there are Win 7 64bit drivers for it so it appears it would work with win 7 but no sign as to why it wouldn't install. No individual USB drivers. Expect they are part of chipset drivers.
Do you have latest BIOS as it seems there are improvements in the more recent versions - none mention win 7 though: https://www.asus.com/us/Motherboards/PRIME-B350-PLUS/HelpDesk_Download/
Win 10 should work as its a brand new motherboard and Win 10 knows what USB 3 is without needing drivers. Make sure to use a new ISO from MS, just to make sure it does know your motherboard.