The DR number, Diederich Rank, refers to the highest number in Diederich's frequency listing, which you can see here: Diederich Ranking.
DR 180. Agere sequitur credere. ~ Note: Here the infinitives are functioning as verbal nouns. The idea is that you have to have faith first, and action then follows: Agere (action) sequitur credere (believing). This is a phrase most often associated with theology, so the believing here is a matter of religious belief.
DR 180. Noctem dies sequitur. ~ Note: You can find this saying in Seneca's reflections on nature in one of his Epistulae ad Lucilium, 107.
DR 182. Non movenda moves. ~ Note: This is one of the sayings Erasmus included in his Adagia, 1.6.61. Note the substantive use of the gerundive: non movenda, "things-that-should-not-be-moved."
DR 183. Artes aliis aliae. ~ Note: This is another of those "aliud…aliud" sayings; in English we might say "Some arts are good for some people, while others are good for other people."
DR 184. In tuum ipsius caput. ~ Note: This is one of the sayings Erasmus included in his Adagia, 4.6.88, and it is a bit like a curse: (may whatever you are doing fall) in tuum ipsius caput. Note the use of the possessive genitive, ipsius, to go with the possessive adjective, tuum; the pronoun ipse does not have a possessive adjective of its own.
DR 185. Plures sunt res quam verba. ~ Note: Note that plus is being used as an adjective here: plures sunt res. The idea here is that language falls short of reality: we can make words and then more words, but there will always be more things than words.
DR 185. Esse quam videri. ~ Note: This is the motto of the state of North Carolina, as you can read about in this Wikipedia article. The quam here expresses the idea of comparison: to be (rather) than to seem.
DR 185. Quis amicior quam frater fratri? ~ Note: Although amicus is more often used substantively, as a noun ("friend"), it really is an adjective ("friendly"). So, as an adjective, it has a comparative form: amicior, "more friendly."
DR 186. Non nova, sed nove. ~ Note: Notice the constrast between the neuter plural, nova, and the adverb, nove: Not new things, but in a new way. You can also find the saying in this form: Nove, sed non nova.
DR 186. Erunt novissimi primi, et primi novissimi. ~ Note: These words come from the Gospel of Matthew, 20; the saying is included by Polydorus in his Adagia, B359. Notice that novissimus here can be translated as "latest" in a series, as opposed to the first in a series (primus) - hence the King James rendering of this verse: "So the last shall be first, and the first last." The Greek reads: οὕτως ἔσονται οἱ ἔσχατοι πρῶτοι καὶ οἱ πρῶτοι ἔσχατοι. Someone's "last words" in Latin are verba novissima.