Bad crank sensor, CKP sensor, should cause a no start, not a single cylinder misfire.
Compression test might be a good idea but from the description that it ran OK after a repair I would think compression wouldn't be the problem, more symptomatic of fuel or spark issue.
I am assuming an SOHC 4.0l engine, as that was standard in the '01 Edge
The SOHC engines used a slightly longer spark plug than the earlier OHV 4.0l, the shorter plugs would work but would cause misfiring, but not just on #2.
Only use Motorcraft plugs in 4.0s they will eat anything else, correct plug for SOHC 4.0l is Motorcraft SP498 (Platinum).
If you didn't change the spark plugs yourself, or even if you did, it might be worth while to pull out #2 plug and make sure it's the right plug and just to see its condition.
If it looks very clean then you may have a coolant leak in that cylinder causing the miss fire, they can start off small and not cause overheating.
Pull #1 or #3 plug to compare with #2's condition.
If #2 shows a blackish residue then fuel injector might be stuck partially open, causing a misfire
To diagnose I would put a timing light on #2 spark plug wire and see if it is firing regularly, not missing a beat now and then, or get an old spark plug, widen the gap a little and connect it to the #2 spark plug wire and a good ground(I use a jumper cable to ground and to hold the spark plug).
If spark seems to be consistent then I would move to test the injectors.
Remove all 3 the injector connections on the #2 bank, use an ohm meter, low setting, 200, and test all 3, should be 11-18 ohms, if #2 is not in the same range as 1 and 3 then replace it.
If it tests OK then you will need to get a Ford compatible Noid Light, this is a light that plugs in-line with a fuel injector, it flashes when injector fires, same as testing the spark plug for consistent firing, no gaps or out of rhythm flashes.
As a heads up, on some Ford PCMs(computers) it will shut off the injector(so no light) if it detects spark plug misfire, this is to prevent unburned fuel from ruining the Cat converter, but you should have seen inconsistent spark if this was the case.
If the spark plug test or the Noid Light test shows missed firings then either PCM or its signal source is the issue.
If spark and Noid light show no issues then injector could still be bad, not opening enough.
You can swap #2 and #1 injectors and see if misfire moves to #1, or you can replace the injector, but that costs money and may not be the problem.
And as an FYI, you should always disconnect the neg. battery terminal when doing engine work, while it is a safety procedure it also resets the PCM, and if you have changed anything the PCM will relearn the new changes.
More than a few times people have changed sensors and still had the same problem, this is because the PCM was still using the old sensors data, so they fixed the problem they just didn't know it, so moved on and spent more money, until they unhooked the battery at some point and problem was fixed, but from the first thing they did not the last
