Learn Portuguese (Portugal): A quem deste o livro?

In English, we often put the preposition at the end of a question (Who did you give the book to?). In Portuguese, prepositions like a (to) must always come directly before the question word. So, you literally ask 'To whom did you give the book?' (A quem).

Which verb is deste and who is doing the action?

Deste is the past tense (pretérito perfeito) of the irregular verb dar (to give). The -ste ending specifically means 'you gave', matching the informal tu.

Do I need to include tu to say A quem tu deste o livro?

You can include it, but it is not necessary and is usually left out. The unique verb form deste already makes it perfectly clear that 'you' are the one doing the giving.

How would this sentence change if I wanted to use the formal 'you'?

If you want to be more formal and use você, you must change the verb to match. The past tense of dar for você is deu, making the sentence A quem deu o livro?