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The shape of your mouth and tongue position isn't really about tones. It's more that Mandarin has a bunch of sounds that aren't used in English. It's difficult to even hear them at first. For example, x versus sh, j versus zh, or ü versus u.

This is technically true but in real life people mispronounce tones all the time and get understood fine. Mandarin songs have no tonal distinctions at all and nobody has problems understanding them. Getting tone right is super important if you want to be extremely terse (as is traditional) but you can get away with a lot of tone mistakes if you add context. (I'm also learning Mandarin at the moment, as my fifth language)

You are describing different vowels and not tones. Different vowels are pronounced by changing the shape of the mouth; tones are produced by the laryngeal muscles, like when you hum a tune.

That's cool, thanks. I learned something.