Do wifi cards on client devices adjust tx strength depending on signal?
Yes the Tx level starts at max power are  then reduced if the RSSI values are high enough to conserve energy and then reduced bit rates at max power if the error rate is too high.  The same is true for mobile phones near towers and fringe areas. But I won't get into the protocol for doing this and RSSI levels are normally not available to the user but are available with special utilites under Windows and other operating systems.