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Your car has a few different codes, but I believe that only one of them is responsible for the car shutting down on you. The P1382 code you have is almost always a defective distributor assembly, but it can be a bad Engine Control Module or broken/jumped timing belt. If you have access to a volt/ohm meter and a test light I can give you some tests to run to verify a bad distributor.
The P1259 code is for "VTEC System Malfunction (Bank 1)", this is most often caused by a low oil level or old oil with the next most common cause being a faulty Vtec solenoid.
The P0401 code is for "EGR System Insufficient Flow Detected" this won't cause your car to shut down but will increase exhaust emissions and could reduce fuel mileage, it is most often clogged EGR passages and is sometimes bad EGR valve, but the EGR passages on these engine clog some easily that I would start by cleaning them.
The P0420 code is for "Catalyst Efficiency Below Threshold (Bank 1)" this again won't cause then engine to stall or keep it from starting. This code could be caused by your EGR problem but it is mostly likely a bad catalytic converter, it's job is to clean the exhaust to reduce emissions.
I hope I've been able to answer your question, if you have any other questions or if you would like more information on your current question please feel free to ask.
Ok there is a 4 wire connector going to the distributor, if you unplug it a test light should light on the BLACK/YELLOW wire when the key is in the on position, this wire gets power from fuse #11 in your underhood fuse box.
Next you will need your ohm meter, looking at the plug on the distributor with the locking tab facing up the 2 right side terminals are for the cam sensor in the distributor, the resistance between these pins should be(###) ###-####hms, and each pin should have OL or infinite resistance to the negative battery terminal.
If everything checks good here then the problem is most likely in the Ignition Control Module in the distributor, these have a very high failure rate, the next suspect would be a missing signal from the Engine Control Module or a wiring problem between the ECM and distributor but these are both fairly uncommon.