Abbiamo salutato l’autista con la chitarra in spalla e la cravatta allentata dopo il concerto.

Abbiamo salutato is the passato prossimo (present perfect). It’s formed with:

• the present tense of the auxiliary avere (noi abbiamo)
• • the past participle salutato (from salutare).

In Italian, professions often take a definite article when referring to someone specific: l’autista = “the driver.” Because autista begins with a vowel, il elides to l’. If you meant “a driver” in general, you’d say un autista.

The preposition con introduces accompanying circumstances—how the driver appeared when we greeted him:

• “with a guitar on his shoulder
• and a loosened tie.”
  This construction shows two simultaneous states or features.

Italian uses the idiom avere qualcosa in spalla to mean “to carry something on one’s shoulder.” While sulla spalla (“on the shoulder”) is grammatically correct, in spalla is the fixed, more idiomatic choice.

Most descriptive adjectives follow the noun in Italian: la cravatta allentata. Placing adjectives before the noun is possible but often changes nuance or sounds poetic/literary. Here, the post-nominal position is standard.

Yes. Italian adverbial time phrases are flexible. Neutral word order puts dopo il concerto at the end. For emphasis or variation you could write:
Dopo il concerto, abbiamo salutato l’autista…

With dopo + noun of time, you normally pair it directly with the definite article when specific: dopo il concerto.

• Dopo di is used before pronouns (e.g. dopo di me) or infinitive clauses (dopo di aver parlato).

Italian adjectives must match the noun they modify. Cravatta is feminine singular, so the adjective is allentata (fem. sing.). If it were plural, it would become allentate.

No comma is required. Italian commas are more sparing than English ones. You could add a comma for a stylistic pause—…, dopo il concerto.—but it’s not mandatory.