Try to further isolate the issue by connecting just mouse+SSD and then just keyboard +SSD and check the behavior. Also try connecting USB devices to other ports.
Since when did this problem start? Did you make any modifications to BIOS like overclocking?
What happens when you just load Optimized Defaults in BIOS (I guess you need to explore BIOS to find if any such option exists)
If Mouse + SSD boots but KB+SSD does not then may be something is wrong with the keyboard interface.
Also check if there are any settings related to USB controllers in BIOS and explore those settings, try to enable/disable/alter those settings wherever possible and retry.
The behavior #1 when no SSD/KB/Mouse it goes into BIOS, I am not too sure if it's a fault or behavior by design for newer UEFI Firmware's. Traditionally it should not enter BIOS unless asked to do so. But concepts and tech changes fast!
If tryouts isolate USB keyboard, then you can give it a try with PS2 keyboard, try to borrow one from someone you know or a nearby computer repair shop.
Also just hook a pen drive to a free usb port and see the behavior.
One risky option is to check if BIOS update is available and flash it to latest. But if your board does not have recovery options or dual BIOS and you don't have UPS/Invertor then in case of any power failure during the process, you may end up bricking the board.