There's no harm in sending the post version ahead and then trying the online when the time window opens up. If it works, great, your post is redundant, and if it doesn't work, your post covers your report.

Same fine regardless how late you are. So, if you've already missed your date cutoff, just forget about it until you need something from immigration next time.

It dislikes Chrome as well.

Props for the REO Speedwagon reference.

They'll guide you.

You fit number 8 on the list with your work permit, which should only be issued to you with a valid non-B and usually a visa extension and reentry permit. Unfortunately, as Robert says, the only way to get the Cert of Entry is if your local embassy issues it to you, and if they disagree in interpretation of the policy above, you have a difficult situation. They also control the passenger list for the repatriation flights, so they also need to allow you a spot on a repatriation flight. Normal commercial flights will not accept incoming passengers until the CAAT opens for arrivals.

Not without re-entering using the card.

My thought as well. That's only a 3wk gap you're trying to bridge. Do a border run by air if you're paranoid.

US gets visa exempt entry for Korea, no issue there. Depending on your layover length, go take one of the free airport transit tours, or bus into the city and explore on your own. ICN is one of the most inviting airports in the world for layovers.

US APEC carries only the benefit of being able to use the Apec priority lanes. No visa benefits whatsoever in any country. As a US passport holder you would receive a standard 30day exempt entry unless you had another actual visa.