The DR number, Diederich Rank, refers to the highest number in Diederich's frequency listing, which you can see here: Diederich Ranking.
DR 172. Genus est mortis male vivere. ~ Note: Note that the infinitive phrase "male vivere" is nominal here, the subject of the sentence, with "genus mortis" as the predicate noun phrase.
DR 173. Quis sine amico vivere possit? ~ Note: Note the subjunctive here: possit. This gives the question a hypothetical quality: Who could possibly live without a friend?
DR 173. Habes amicos, quia amicus ipse es. ~ Note: The pronominal ipse here agrees with the implied subject of the verb: quia (tu) ipse es amicus.
DR 173. Unus amicorum animus. ~ Note: The genitive expresses the idea of possession: There is one mind of friends = Friends have one mind.
DR 173. Unus Deus, et plures amici. ~ Note: This is one of the sayings Erasmus included in his Adagia, 3.4.88.
DR 173. Multus amicus, nullus amicus. ~ Note: Compare this similar saying: Amicus omnibus, amicus nemini. The idea is that someone who has too many friends is really no friend at all.
DR 173. Amici nec multi, nec nulli. ~ Note: Compare the saying in the Adagia of Erasmus, 3.6.37: Neque nullis sis amicus, neque multis.
DR 173. Nec nulli sis amicus, nec omnibus. ~ Note: If you are friendly towards someone in Latin, that requires the use of the dative as you can see here: omnibus is dative plural, and nulli is dative singular. Note also the nec... nec... construction, which is equivalent to "neither... nor..." in English.
DR 175. Vox unius, vox nullius. ~ Note: The Latin word "vox" expresses a whole range of meaning, including what we call "sound" in English, as well as "voice" and also the idea of "word" (hence "vocabulary," referring to a collection of words).
DR 176. Audiatur et altera pars. ~ Note: Note the subjunctive: audiatur. The word "et" is being used adverbially here: Let the other side also (et) be heard.