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Not enough info. But if you are moving that fast it is likely not second gear. Could be a failing overdrive clutch, TCC lockout solenoid. Torque converter, or an electrical issue. If the check engine light is on that may help.
You may want to be careful before proceeding with small claims court. There are MANY variables to the equation. It depends on what they sold you and why. If you still are having issues with the vehicle let me know.
Overfilling the pump would not break it. It would just result in a large fluid mess as the excessive fluid would be pushed out the cap. If the engine was ran long enough with the fluid level low that could have ruined the pump. Allow the fluid to settle...engine off...then recheck the level running and see if you have any assist. If you still do not have any assisted steering you will want to have the system checked. If the system is moaning, cycle the steering back and forth several times from stop to stop. Recheck the fluid level until full. This should bring back the steering assist, otherwise you may need a pump, a steering gear, or possibly both. Hope this helps.
Those are multiple issues, likely not related, but they possibly could be. The keyless entry system will malfunction if a latch position switch is faulty, from a defective module, or from a bad power or ground to the module. The tire monitor system on most vehicles uses it's own module and if the tires are all set to the proper inflation will require a sensor, module, of re-calibration, or perhaps all of the above. Both systems should provide some DTC information if scanned with the proper equipment. Unfortunately there is probably no "quick" fix to either. The systems will need to be scanned and then the faulty components tested and replaced. Sounds like the locks would be the higher priority as that situation could result in keys locked in the vehicle, battery drained, etc. Sorry I can't be more help online, but I will gladly take a look at it if you would like.
Your Honda uses a "captive" rotor design. In order to service the front rotors the bearings will be required. It is a bit more work than a standard brake job.
13 volts is likely not enough. The system needs to be tested under load to properly gauge the output potential of the alternator. Was the light on before installing the battery?
As the professor said, the Accelerator Pedal Position(APS)switch has been a known problem. I also would be very interested in putting a scope on that Crankshaft Position Sensor. Checking the basic's such as the battery posts and connections would also be prudent. I would hope that they have already done these things, but you never know. If you are still having issues after this visit to the dealer let me know and I would gladly take a look for you. Feel free to give me a call today if you want to discuss your problem.
If you are still experience heating issues and have had the stat replaced, heater core is the likely suspect. I see issues with the cores often at the shop.
Did you resolve the red light issue?
Did you figure out if your plugs were still original equipment?