Learn Italian: Lei beveva spesso il tè con la principessa? - Did you often drink tea with the princess?

Exactly, but bere (to drink) is an irregular verb. In the imperfetto, it uses its old Latin stem, bevev-. This gives us the forms bevevo, bevevi, beveva, and so on. Since the subject here is the formal Lei (you), we use the third-person singular form.

Why does the sentence use Lei when the English translation says "Did you..."?

In Italian, capitalized Lei is the formal way to say "you". It is used when speaking politely to someone you don't know well, an authority figure, or in a professional setting. Because it functions grammatically just like the word for "she", it takes the third-person singular verb beveva.

Why do we use the imperfetto (beveva) here instead of the passato prossimo (ha bevuto)?

The biggest clue is the word spesso (often). The imperfetto is the past tense used to describe ongoing, repeated, or habitual actions (things you "used to do"). Because the speaker is asking about a recurring habit in the past, the imperfetto is required here.

Why does spesso come right after the verb instead of before it like in English?