Is there any chance of eye infection from using a viewfinder? If so how can we get rid of that? How can we clean a viewfinder?
Well, the viewfinder itself is not going to cause infections, but some of the germs that cause conjunctivitis are highly contagious. If you're passing your camera to people with red eye, ask them to wash their hands and to use the LCD screen instead.
In general, though, these germs are not particularly long-lived away from a human host. Just letting the camera sit for a while will basically do it. I'm sure there's a chance of some more rare disease, and you could carefully clean the viewfinder area with lens cleaner, which is generally alcohol-based and will serve as a disinfectant.
Are you passing your camera to potentially-unhealthy strangers very frequently? In general, people usually trust others to not walk around when they're really sick, and trust in their own immune systems to deal with the rest.