Questo bicchiere è così trasparente da sembrare invisibile, un vero esempio di eleganza.

The construction così … da + infinito expresses “so … that …” in Italian.

• così trasparente = “so transparent”
• da sembrare invisibile = “that it seems invisible”
  It’s equivalent to English “so transparent that it seems invisible.” You could also say tanto trasparente che sembra invisibile, but così … da is more concise.

In Italian, to link a degree expression (così, tanto, talmente) with an infinitive result, you use da + infinito.

• così trasparente da sembrare…
  You don’t use per + infinito here, because per would express purpose (“in order to seem”), not consequence/result.

Yes, you can say così trasparente da apparire invisibile.

• sembrare and apparire are often interchangeable: both mean “to seem/appear.”
• apparire can sound slightly more formal or literary, while sembrare is more neutral and common in everyday speech.

Both di eleganza and d’eleganza are correct; dropping the vowel in speech and writing (to get d’eleganza) is optional and mostly stylistic.

• di eleganza (no contraction) is perfectly standard.
• d’eleganza (with apostrophe) can feel a bit more literary or poetic.

The comma introduces an apposition or parenthetical remark that adds extra commentary.

• The main clause is Questo bicchiere è così trasparente da sembrare invisibile.
• Then you append un vero esempio di eleganza as an extra judgement: “a true example of elegance.”
  Without the comma it would read as one continuous phrase, but with the comma you emphasize it as a concluding flourish.