You must be joking. Mandarin is not a written system at all. Even though I don't have the passion for HongKong pop music, I have no problem understanding traditional writing at all, cause it is just so similar to simplied one.

Of course Mandarin is a written system. Pop music from Hong Kong is usually in what basically amounts to Cantonese-pronounced Mandarin. That's why they sing 是 instead of 系 and it's why people recommend NOT using pop music as a learning tool when learning Cantonese. Written Cantonese also exists: 係唔係佢哋㗎？ vs 是不是他們的？, for a Wikipedia example. The first is what people speaking Cantonese actually say, the second is what they might write if they're trying to be formal or official and it's probably what you're used to seeing.

> No, people from Beijing cannot read a text written in Shanghainese using simplified script.

I'm not a native of Shanghai but I still get to understand written Shanghainese. Because even though I can't _read_ it, I can somehow _interpret_ it. It uses the same Chinese characters and I already knew what these characters mean.

> Since everyone in China is taught mandarin Chinese they tend to write to each other in mandarin.

There are still people native to Cantonese, Min Nan, or Hakka who don't speak Mandarin.