Keys found on ADB keyboards but not found on pre-ADB keyboards will still work. The system software still understands the key scan codes. For example, the Plus and earlier keyboards lacked the Control key. The control key on the ps2 keyboard connected to the adapter will still work as expected on pre-ADB systems.
The adapter board connects to the bottom of the discovery board (the side with the longer pins), and the PS2 connectors belong on the same side as the discovery board's USB connector.
The adapter is composed of an entirely passive PCB with all the connectors that attaches to the headers of an stm32f0discovery board. The connector PCB can be separated easily, and the stm32f0discovery board can be used for other purposes, or if the connector PCB is revised, the revised board can be swapped on.
The discovery board uses USART2 to send diagnostic information. It is set to 8n1 9600 baud. USART2 is pins PA.2 (TX) and PA.3 (RX). They're of course TTL level signals, so you'll need a TTL serial adapter.