I'm getting a new folding bike and I've been thinking about fenders for one purpose - to protect the bike and not to protect myself. I won't be installing a rear fender on my bike due to various technical reasons - but I've been thinking of installing a front fender. It seems as though the purpose of the rear fender is mainly to protect the rider from the dirty water where as the front fender seems to serve more of the purpose of protecting the chainring and important elements of the bike.

So my question is:

1. Is the rear fender protecting important elements of the bike? How so?
2. If I can't install a rear fender, would I benefit in protecting the bike by installing just a front fender?