You've got some very soft tap water. Are you adding any additional trace minerals?
To answer your questions:
Should I medicate based on the symptoms (white spots, runt with heavy breathing, not growing well)? The white spots could be an indication of a problem but in most cases, a salt dip will remove the spots. Make sure you return the fish to a hospital tank for further observation. Also, if the problem is in the main tank, you'll eventually have to treat the main tank and the tetras are sensitive to most treatments so take that into consideration.
Are stressbars normal for some strains and are they due to stress only, could the discus be excited? Yes, the stress (mood) bars are normal for those type.
Are strange feces normal after bloodworms? Yes, they expel the bloodworm casings so the feces look clear and stringy.