Learn Italian: Fosse per me, ci si sveglierebbe più tardi in questo ritiro. - If it were up to me, one would wake up later in this retreat.

Fosse per me is a common fixed phrase meaning "if it were up to me." You absolutely can say se fosse per me, but Italians often drop the se in this specific idiom. It uses the imperfect subjunctive (fosse) because it describes a hypothetical, unreal scenario.

Why is it ci si sveglierebbe instead of just si sveglierebbe?

The verb here is svegliarsi (to wake up), which is reflexive. When we want to make a reflexive verb impersonal ("one wakes up"), we need to combine the impersonal pronoun si with the reflexive pronoun si. Since si si sounds awkward, Italian changes the first one to ci, resulting in ci si.

Since this lesson is about compound tenses, how would I say "one would have woken up" here?

You would say ci si sarebbe svegliati (or svegliate for an all-female group). In compound tenses with the impersonal si or ci si, the auxiliary verb is always essere in the third-person singular (here, sarebbe). However, the crucial rule is that the past participle must take a plural ending (-i or -e).

Why is sveglierebbe in the conditional mood?