Another pronunciation trick in your initial learning of a new language: Study and mimic the heaviest accent in your own language, by a native speaker of the language you wish to learn. If you are a native English speaker, you can master new mouthshape combinations relatively quickly by (for example) mimicking a heavy Arabic accent in English. This helps train your mouth early to try on and get comfortable with a new pronunciation repertoire. Once you cultivate a new accent in your first native language, you can very easily graft it into a new language you're learning, and reinforce your ability to sound more "native" and fluent from the outset.
The short answer: yes. That's why syllables are often spread over two notes, to convey rising and falling tones. However, in the 20th century when they started importing pop songs from other countries, particularly Japan, they translated the lyrics and just did the best they could. The vocabulary of pop tunes is pretty limited so they don't really have a lot of trouble understanding them. Soon they began writing their own pop tunes with no regard for tone correspondence. I used to go to Chinese movies with my Sichuan girlfriend in the 1970s, and even with my modest command of Mandarin I could understand some of the song lyrics. Of course it's easier for a foreigner because we never develop the same tight synapses for tonality that native speakers do. I could sometimes follow her conversations in Sichuan dialect, which has six tones in addition to some simple consonant shifts, and that's something people from Beijing have to struggle to learn to do.
