Rummy Nose Tetra Unusual Behavior

Losing red in the face area is just like fading colors on other fish. Fading is a sgn of distress.

From the fading and him darting around and breathing rapidly is a sign he is very stressed out.

Just from the info given, we cant tell for sure if he also has a disease.

Usually sick fish don't stay around the group, but since he sounds to be moving around a lot, it doesnt fully sound like he is sick, which a sick fish would normally be withdrawn. He just sounds a lot more stressed/freaked out than the others.

They are new so stress is a given. Fish can die from over stressing so I would recommend doing all you can to minimize stress to give the fish the best chances at calming down. The first fish probably died from overstressing, the other fish also freak out more when they sense/feel another fish is panicking.

You can reduce some stressors by making sure there are enough hiding areas (more plants/decor for darker areas to hide behind/in), leaving the lights off (better yet, cover the tank with a towel or wrap newspaper around it), and also limit your presence to the fish as you are most likely seen as a threat (netting them and your sheer size causes a negative association resulting in stress until they calmdown and learn you are not a danger). The new environment itself is a unknown to the fish so they are still stressed thinking their may be dangers until they settle into their new surroundings, so reducing stress helps them calm down easier.

Disease cannot be determined wuth the given info, but it is not ruled out. Minimize stress, but monitor the fish every so often to check for signs of disease.