Reguarding the OBD II, when the battery is dead or disconnected, any OBD II codes are cleared. In order to pass inspection the car then has to check all OBD II components - that way you can't clear codes just as you drop the car off for inspection without fixing the problem. Driving for a while usually will allow the car to check all its components. A full OBD II drive cycle can be found at this link which also explains more about OBD II - Understanding OBDII: Past, Present & Future An OBD II reader typically can tell you if all the systems have been checked so that the car can be inspected.
As others have already discussed, the wrench is just a service reminder.