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Mandarin is understood. Many shopkeepers and sales people speak some broken Mandarin, because there are lots of mainland Chinese tourists.
As a tourist, I believe you can even just use English, depending on where you are.
Yes, two dialects (Mandarin and Cantonese) with the same writing system. It's the difference between 语 and 文. I think the only difference is that they use traditional characters more so than simplified characters. But it looks like you are learning the traditional characters, so you should be good with the writing system there.