As far as I know, the front wheel speed sensor is part of the hub assembly. Talk with your local parts store to confirm this.
It is not uncommon for the EGR passage at the intake manifold (behind the throttle body) to become plugged. Commonly, the throttle body and EGR valve will need to be removed to clear the passage. I do not recall a P1113 code for this vehicle, perhaps you have the number wrong. It sounds like the cooling system needs a good flushing to remove all the brown sludge. If the engine is still overheating once that is done, the cooling system should be properly diagnosed before any repairs are made.
I have seen problems with backlighting failure on the dash & switches. Most commonly the affected component will require replacement as individual bulbs are not easily replaceable.
You can check recalls on the RepairPal site, here is the link - http://repairpal.com/chevrolet-hhr-2007/recalls
The RepairPal estimator indicates the $150 estimate is a bit high, (http://repairpal.com/estimator/results) perhaps there are some diagnostic charges includes in your estimate.
The problem could be with the anti-theft system. Please visit the following link for more information: http://repairpal.com/car-wont-start-because-of-anti-theft-system-that-uses-raised-chip-key-032
The temp gauge signal comes from the PCM which relays the signal from the engine temperature sensor. I would suspect the temp gauge is no longer working due to an internal cluster fault. If the coolant sensor signal to the PCM is OK when monitored with a scan tool, repair or replacement of the instrument panel cluster will be necessary. Please note if the original cluster is repaired, no programming should be necessary. If the cluster is replaced, the new cluster will require programming.
If you cannot pull the key out with a pliers, The lock cylinder will need to be removed and disassembled to remove the broken key.
It is not uncommon for the temperature gauge to rise a bit when the vehicle is stopped, before the cooling fan turns on. If the gauge is going in to the red, it could be that the electric cooling fan is not working properly.
Your warranty company may be calling the hydraulic valve assembly the "ASE Control Unit" and the electronic brain the "ABS Module" But these names can be used interchangeably. I would recommend you have your insurance company explain what they mean by "ABS Control Unit".