Learn Italian: Ho creduto che noi fossimo più spontanei e spiritosi. - I believed that we were more spontaneous and funny.

The main verb Ho creduto expresses a personal opinion or belief, which triggers the subjunctive in the following clause. Because the belief took place in the past, we use the imperfect subjunctive (fossimo) to describe an ongoing state that was happening at the same time.

Since Ho creduto is formed with the present tense of avere, why don't we use the present subjunctive (siamo)?

Even though it uses a present tense helper verb, the passato prossimo (ho creduto) counts as a past tense because it describes a completed past action. When the main clause is in a past tense, the dependent clause must shift to a past time frame too, requiring the imperfect subjunctive.

Is the pronoun noi strictly necessary before fossimo?

It is not grammatically necessary because the ending of fossimo already tells us the subject is 'we'. While pronouns are highly recommended for singular imperfect subjunctive forms because they look identical (e.g., io fossi, tu fossi), fossimo is completely unique. It is included here mostly for rhythm, flow, or a slight emphasis.

Does spiritosi mean 'spiritual'?