Dopo cena si richiude il tappo della stessa bottiglia per conservare il vino.

The si here is the impersonal/passive si passivante. It doesn’t refer to a reflexive action, but rather turns the verb into “one closes again” or “the cap is closed again.”

• Structure: si
  • 3rd person singular verb + subject
• English equivalent: “You re-close the cap” or “People re-close the cap”

In Italian, certain time expressions drop the article.

• Dopo cena = “after dinner” (general period)
• If you say dopo la cena, it’s still correct but slightly more formal or referring to a specific dinner event.

Yes. Both are correct:

• Dopo cena (common in spoken Italian, general sense)
• Dopo la cena (adds the article, sounds a bit more specific or written)

Stessa emphasizes that it’s the same bottle you were already using.

• Word order: Normally you say la stessa bottiglia, so in the full phrase it becomes il tappo della stessa bottiglia.
• You could also say il tappo della bottiglia stessa, but that’s less common.
• Alternative with a demonstrative: il tappo di quella stessa bottiglia (“that very same bottle”)

Per + infinitive expresses purpose in Italian, equivalent to English “in order to” or just “to.”

• per conservare il vino = “to preserve the wine”
• Alternative: affinché si conservi il vino (using a subjunctive clause), but per
  • infinitive is shorter and very common.