Yes, the back of your nose is connected to your 'windpipe' so just as you can breath through your mouth and nose you can vomit through your mouth and nose, although vomiting can usually be quite a violent reaction so it will normally take the path of least resistance, i.e. through your mouth.
Your beagle's nose should be slightly wet if it is dry it might be sick or something like that and consider taking it to the vet
Your nose has a defense mechanism that protects against pathogens: hair and mucus. The hair in your nostrils helps catch airborne bacteria as you breathe in and out of your nose. The mucus passes through the hair in your nostrils, and then, when you blow your nose, the mucus contains pathogens that make you sick. This is not a 100% effective system, because people get sick all the time.
Yes that is what the term STD (sexualy transmited disease) refers to.
Your ferrets nose should be dry.
i don't know but you must be sick.
its not sick its just unhealthy
Yes, you can get sick from a hamster as long as it has something contagious (like a cold, flu, etc).
If your dog is doing that he probably just wants something like food or to go outside!
hazardous wastehazardous waste.
Hazardous waste.
you can get sick if you do from the mouth
No. The tiny hairs (cilia) in your nostrils collect input as well as output.