Please understand that, just because we say something a particular way in English, doesn't mean other languages have to say it the same way in their language. I speak Spanish and many times the sentence is backwards, or does not translate to exact English. They are different languages for a reason.
This lesson has a lot of "bring me" and "give me" phrases. Even though "please" is included, that still sounds rude to me. I don't tell waiters "bring me [thing], please". I always say "could you..." "would you...", just a gentler-sounding way to make a request in English, I think.
What's the culture and expectation on the matter in Ukraine?
"будь ласка" = "be a blessing" => "please" serves as the modifier making this a polite request. If you literally say "would you" in Ukrainian, it comes off as a suggestion, a wish for something not expected to be immediately feasible, or as a polite reminder.
Notice that Дайте has the the polite, formal you (or you plural) imperative conjugation. Not the familiar/informal you.
In order to avoid the imperative conjugation, you can say "Прошу дати" = I beg/ask (you) to give => Please give.
Without the specification in "Дайте" it can mean "give me" or "give us" (if someone is speaking on behalf of many people). It cannot mean "give him" because then it would be "дайте йому", we would not skip the pronoun in that case. We skip it only when we mean, give it to the one speaking, to me (or us).