It’s difficult to explain. Hopefully an expert will post a reply too. Your sentence needs a comma there because “with Hungary” is an introductory phrase. It is also a fragment. The meaning of your sentence is exactly the same if you put the fragment at the end (“The question is a little different with Hungary.”) If you use a fragment at the beginning of the sentence, you will need a comma to separate it from the main sentence. Why? It signals to the reader or speaker that the main part of the sentence is coming next. Word order is less flexible in English than Slavic languages and we use commas to break up long sentences into something easier to understand. Sometimes we use introductory phrases and commas just to change the rhythm of speech or writing. It’s more about intonation, pacing, and style than simply grammar. More examples: - At my school, we don’t teach that subject. - On the shelf, look behind that book. - If my door isn’t open, you can ring the bell. - In English, we use commas in mysterious ways

You absolutely do NOT need a comma after Hungary. You do need the comma after "different". The comma after Hungary is helpful (though optional) because it gives the listener (or the reader) time to prepare for the independent clause that follows.

I don't think it's needed. It depends on the context. Putting a comma after "Hungary" isn't needed grammatically. It is one way of giving the word "Hungary" a little emphasis. When speaking, you might pause slightly after Hungary for emphasis. If so, you might do the same thing in writing with a comma. It would be particularly appropriate if the previous material had mentioned other countries, and Hungary was being set off as an exception. "There is one answer for Austria, Germany, or Poland. With Hungary, the question is a little different...."

It's a question of style. A newspaper or publisher with a minimalist punctuation style might not include it. Another would. Although there is no ambiguity in this example, there might be in another, so it could be safer to include it. I believe this is a fronted adverbial like 'In 1980,' or 'Before evening.'. The more usual word order (SVO) here would be 'The question is a little different with Hungary', so you are also marking that.

Вітаю, Андрей! Я учу украинский язык и испытываю симпатию к вашей стране. Практически все мои предки из Украины, сам я из Ростовской области. Я ищу собеседника, чтобы учиться украинскому языку. Мы могли бы также практиковать английский вместе. Надеюсь, политика не помешает нам пообщаться. Как на это смотришь?