Hi Lou and welcome!
I looked at the Nikon site and they list a filter set (includes a UV, circular Polarizer, Neutral Density 4 and Neutral Density 8 filters) available for your model digicam. These filters require the use of the HN-CP10 Lens Hood therefore they need to be 77mm. I suspect this is because the lens extends. Also the 77mm may help avoid vignetting when shooting wide angle shots.
Unfortunately I don't have first-hand knowledge of this camera model so I can't help you with the other questions in your post. Sorry. Perhaps someone else reading this will join in with the answers.
