Pensavo che il mio profilo fosse privato, invece le foto erano visibili a tutti.

Pensavo is the imperfetto. Here it describes an ongoing mental state or belief in the past: I thought / I believed / I was under the impression.

If you said Ho pensato, it would sound more like a completed thought at a specific moment: I thought or it occurred to me. In this sentence, the speaker is describing what they believed before discovering the truth, so pensavo fits better.

After pensare che, standard Italian normally uses the subjunctive in the subordinate clause, because it expresses a belief, opinion, or assumption rather than a fact.

So:

• Pensavo che ... fosse ... = standard Italian
• Pensavo che ... era ... = heard in informal speech, but not the standard choice

Because the main verb is in the past (pensavo), Italian uses the imperfect subjunctive: fosse.

Fosse is the imperfect subjunctive of essere.

In this sentence, it corresponds to English was, even though English does not usually show the subjunctive here.

So:

• è = is
• era = was
• sia = be / is, in the present subjunctive
• fosse = were / was, in the imperfect subjunctive

Here, fosse does not mean something special like would be. It simply appears because of the grammar after pensavo che.

In Italian, possessives usually take the definite article.

So Italian says:

• il mio profilo
• la mia foto
• i miei amici

English does not use an article here, but Italian usually does. The main common exception is with many singular family words, such as mia madre or mio fratello.

Because le foto is plural, the verb must also be plural.

So:

• la foto era = the photo was
• le foto erano = the photos were

Italian verbs agree with the subject in number, just as in English.

Foto is short for fotografia. It is a feminine noun, and its shortened form does not change between singular and plural.

So:

• la foto = the photo
• le foto = the photos

This is why the article tells you whether it is singular or plural.

Because the adjective has to agree with le foto, which is plural.

So:

• la foto era visibile = the photo was visible
• le foto erano visibili = the photos were visible

Visibile is singular.
Visibili is plural.

Invece introduces a contrast between expectation and reality.

In this sentence, it means something like:

• instead
• but instead
• whereas in fact
• actually, on the contrary

It signals: I thought one thing, but the opposite was true.

Literally, a tutti means to everyone or to all.

So visibili a tutti literally means visible to everyone. In natural English, in this context, it often means viewable by everyone or public.

No, visibili a tutti is the natural choice here.

With visibile, Italian uses a:

• visibile a tutti = visible to everyone

Per tutti usually means for everyone, which is a different idea. So it would not sound right in this sentence.

Italian often leaves out subject pronouns when they are not needed, because the verb ending already shows the subject.

So pensavo already means I was thinking / I thought. Adding io is possible, but it is usually only done for emphasis or contrast.

Yes. Here privato means private, as in not public.

It agrees with profilo, which is masculine singular:

• il profilo privato
• la pagina privata

So fosse privato means was private.