Are my poppy seedlings dying? I leave the plate filled with water everyday. How can I save them? (Even if it means ripping some off and leaving them more spaced out.)
It seems fairly likely the problem is water. It may be too little but it also may be too much.
Stormy's spray bottle approach is wonderful for seedlings, and I too would do that.
But do not! leave standing water in the bottom of the tray. If the water doesn't soak into the soil and leave the tray dry within, say, an hour, there is too much water. If so, temporarily take the plant pot out of the tray, dump the tray, and put the plant pot back. If the tray fills yet again from the pot draining out, (1) do it again, and (2) that's a nearly certain sign that watering is excessive.
It can be interesting to put a bit of dirt in a pot then leave it for a couple days in a shallow pool of water. Then tip it out and see how sopping wet the mud is at the bottom, with too little room for the air that roots need also.
P.S. Why do you think they are dying? My vision isn't the best but they look pretty good to me - maybe a bit yellow.