They are etiolated, i.e. stretched, from insufficient light. They also look very wet. Do the containers have drainage holes?

Yes but I can make sure the holes are large enough and are working. I do have the light just a few inches above the plant, but I will actually measure to make sure it's no more than 2 inches.

If I enlarge some drainage holes and get these leaves to be less than 2 inches from the light, is that my best chance to prevent this problem from worsening?

Am i correct that the 2 which fell, are dying/dead?

I moved them an inch away. I increased the hole sizes in the bottom of the container.

Should I offer any support for the remaining stems?

They're not dying just weak from not enough light. If they get enough light and aren't keept so wet, they should make it. Support shouldn't be necessary.

Thank you jostus.

At what point do I start to harden off? After their second set of true leaves?

My main concern for your seedlings would be damping off, as seedlings are instantly killed by rot when soil remains soggy. As for hardening them, I personally wouldn't wait long. I begin bringing them outdoors at whatever stage ,on days when the weather is calm and in the 60's or above. I place them out in a location sheltered from direct sun and strong wind like a covered deck or patio and away from snails or slugs. I bring them back in when the temperature begins to drop in the evening or earlier during the day if the weather becomes unfavorable. I expose the seedlings to part sun or morning sun once they begin to show a new set of leaves. Upon emergence of the next set of leaves I place them in full sun. Then they go in the ground

How deep is that container? From the photo, it looks only about an inch or so. You may need to pot up the two surviving plants to give the roots room to breathe.