Learn German: Er zeigt der Gemeinschaft keinen Respekt. - He shows no respect for the community.

The verb zeigen (to show) usually takes a dative object to indicate to whom you are showing something. Literally, this sentence translates to 'He shows to the community no respect.' Since die Gemeinschaft is a feminine noun, its article changes to der in the dative case.

Why do we use keinen here instead of nicht?

In German, you negate a noun that has no article (or an indefinite article like 'a' or 'an') by using kein. Since Respekt is being used as a general noun without an article here, we negate it with kein. Because der Respekt is a masculine noun acting as the direct object (accusative case), it takes the -en ending to become keinen.

Is Gemeinschaft always a feminine noun?

Yes! Any German noun that ends in the suffix -schaft (like die Freundschaft or die Gesellschaft) is always feminine. It only uses the article der here because it is in the dative case.

How would this sentence change to say 'They show each other no respect' using the reciprocal pronoun einander?

You would change the subject to plural (sie) and replace the dative receiver (der Gemeinschaft) with einander. The resulting sentence is Sie zeigen einander keinen Respekt. The word einander is very flexible and never changes its ending, so it drops perfectly into that dative slot.