Just keep the duckling warm with good feed and water and hopefully the little one your concerned about will make it. Probably just pooped out from the ordeal of hatching. If you have some Poultry Nutridrench add to their water. It’s a great boost for newly hatched ducklings.
If it’s drinking the runny nose could just be excess water coming out of its nares. As for salmonella don’t let the 3 yr old handle the duckling right now not so much because of sickness although that should be addressed to with hand washing anytime ducklings are handled but because the...