Do all computers/devices connected to an airport extreme run at the same speed?
No - this is demonstrably false for Airport hardware even before the latest generation where 802.11ac is introduced.

Simply connect two or three Mac at different distances (1m, 5m, 10m) and run wireless diagnostic on each.  You will see different transmit rates and MCS index for each device which correlates to how fast the radio link between each device and the base station is based on current interference and signal to noise ratios.