This is a long, tough lesson!!

Question

I’m having a lot of trouble with this lesson. Can you provide parallel examples of ways to say the same thing with “le jour précédant /précédent / le lendemain” and explain exactly what you mean by the rule that some phases can only be used “on their own.” Also, it is unclear whether the plus que parfait is required or whether the passé composé can be used following a phrase.
La veille, nous avions découvert la verité. (example)
Are these correct?
Nous avons découvert la verité le jour précédent.
Le jour d’avant, nous avons découvert la verité.
Nous aurions dû découvrir la verité la veille de son mort.
Nous aurions pu découvrir la verité le jour précédent, mais nous avons raté les indices.
Il a découvert la verité la veille de son mort.

I know that's a lot. Thanks for any guidance.

Answer

My guess is that "on their own" means they must be followed by punctuation rather than by more words.

Answer

Really interesting lesson but I am also unsure what is meant by the 'on their own' proviso.  Perhaps while you can say 'la veille de son départ' or 'le jour précedant son depart' you cannot use 'le jour d'avant/d'après' or le jour précedent' with a noun in the same way?  I would also like to know if you can use any of these terms to talk  about the future as the example 'Tu veux dire ce lundi ou le lundi suivant' suggests you can.