La porta si apre lentamente con la chiave.

It’s neither a full passive nor a genuine reflexive. Grammarians call it an anticausative construction:

• Passive (vera passiva): uses viene aperta (“is opened by someone”).
• Reflexive (riflessivo): the subject and object are the same (“He washes himself”).
• Anticausative (here): the subject experiences the action without mentioning the agent (“La porta si apre” = “The door opens”).

Yes, you can, but with a slight nuance:

• La porta si apre lentamente con la chiave. (anticausative; no agent expressed)
• La porta viene aperta lentamente con la chiave. (passive; still no agent mentioned, but you use the auxiliary venire plus past participle)
  Both are correct; the anticausative is more concise and common in spoken Italian.

Because the subject is la porta, a singular noun. Italian verbs agree in person and number with their subject.

• Singular subject → third person singular verb form (apre)
• If the sentence were le porte si aprono, you’d use the third person plural (aprono).

Both express the instrument, but con + noun is the idiomatic, concise way to indicate “with” an instrument:

• con la chiave = with a key
  Using usando (gerund) is longer and often unnecessary in simple statements:
• usando la chiave opens up possibilities but can feel redundant.

Yes. Italian word order is flexible. For example:

• Con la chiave la porta si apre lentamente.
  This fronting emphasizes the instrument (“with the key, the door opens slowly”). Meaning stays the same, but your focus changes.

Italian often requires the definite article before singular and plural nouns, even when speaking generally or about any such object:

• La porta (the door)
• La chiave (the key)
  Dropping the article sounds odd to an Italian ear. The article is a grammatical necessity, not always a marker of specificity as in English.