Pus is formed when inflammatory cells (usually neutrophils) react to an infection. If there is pus around your dog's eye, it is probably because there is an infection (likely bacterial) around the eye. This should be evaluated by a veterinarian as soon as possible.
This is an indication of an infection in your dog's eye - if it doesn't resolve in a couple of days you should take him to the vet.
If you get pus from a blister in your eye, you should probably see a doctor.
A pus pocket under the eye lid can form if if there is an infection in and around the eye.
A pus pocket under the eyelid is signs of an eye infection.
The green pus is mostly dead inflammatory cells and tends to be non-infectious. However, if the cause of the inflammation in the dog's eye was infectious (bacterial or viral are most common in dogs), that infection is very likely to be transferred to a puppy and you may see similar pus coming from the puppy's eye in a few days. I would suggest taking your dog to a veterinarian if this is new and you aren't sure what you are seeing - there could be a foreign body in the eye or a serious infection that needs to be treated to prevent blindness.
It could have a link, but probably not.
it might be infected
You should take the dog to the vet. If this is happening, he probably has an infection.
It means that your dog either has an infectoin of a type of ocular cancer.
If the bite is on a human, take that human to see a doctor. If the bite is on a dog, take the dog to a veterinarian.