Your cat might be coming down with an upper respiratory infection. The best thing to do for this is to start the cat on antibiotics to prevent a secondary infection.
Sometimes cats can catch a simple cold that results in them sneezing and having a runny nose. This can clear up on it's own. It's always better to take your cat into the vet to be sure.
Nothing. Cats can get colds just like humans and it will probably get better all by itself. If it doesn't, then you can always take your cat to the vet, but a runny nose is nothing to worry about.
