I forgot to mention - before you get too far down the road buy parts / swapping parts in - I'd do a compression test first. Just to make sure that the engine has good compression. If compression is dead or low in any particular cylinder(s) - all this diagnostic work would be just wasted time.
As for the pump noise - this generation has a returnless fuel system - basically, pumps fuel only on demand. So there will not be that tell-tale "cycling noise" that you get with the older fuel injected setups.
But you can still diagnose it like the older ones. First thing I would check is for power running to the pump when the ignition is ON. Just pull up on the rear passenger lower seat cushion (just friction clips in the front), and the lower seat will pop right out, you'll see the wiring running right behind the driver's seat to an access panel on the floor. Just disconnect the connector, use a multimeter to check for voltage - I'd cycle the ignition on and off just to rule out an intermittent issue with the switch.
If that show good voltage - it is possible that the fuel pump itself might be dead or dying. These fully immersed fuel pumps generally do not go bad, unless you have a habit of running the tank as low as possible between fillups, or if you drive in a way where the fuel will slosh away from the fuel pickup (ie, autocross, SOLO cone bashing, etc.)
Fuel filter is actually inside the fuel pump assembly. Debris is usually stopped by the exterior "sock" filter on the fuel pickup. A feature of the returnless fuel setup is that it only filters fuel that will be used - so the fuel filter itself actually sees very little utilization, compared to other setups. Back-cycling feature also flushes out contaminants that would clog other filters - made to last the life of the car, unless you suspect the tank with something other than unleaded fuel (like diesel) or fuel that was heavily contaminated with water, etc.
Great job so far - given all the steps you've done so far - you've pretty much got it narrowed down to potentially the ECM or fuel pump. Hopefully, it will be a case of a bad fuel pump, unusual for this generation, but not unheard of. If pump checks out - leaves the most expensive item on your list. The ECM is a little trickier - might be worthwhile to check on Ebay or your local pick-and-pull to see if you can get your hands on a cheap ECM. I've seen then go for under a $100 - dealership will ding you for about $1800 if you go that route.
If the ECM doesn't do the trick - then you are left with back-tracing the wiring, possible bad crank / camshaft / TPS sensors, etc. Possible VVT-I system failure (timing locked to something funky).