Learn Russian: Это отнюдь не мистика, секрет намного проще! - This is by no means mysticism, the secret is much simpler!

While all three mean "not at all" or "by no means," отнюдь не is the most formal and categorical of the group. It carries a strong literary or intellectual tone, which perfectly fits the contrast with a concept like мистика. It is used to decisively shoot down a false assumption.

Does мистика exactly mean "mysticism" here?

It is a bit broader and more common than the English "mysticism." In Russian, мистика is frequently used in everyday language to mean "magic," "the supernatural," or "something spooky and inexplicable." The speaker is essentially saying "there is no magic involved here."

Why use проще instead of более простой for "simpler"?

Проще is the synthetic (short) comparative form of the adjective простой (simple). In Russian, when a comparative is the main predicate of a sentence (describing what the subject "is", as in "the secret is simpler"), this one-word form is heavily preferred over the two-word compound form (более простой).

Could I use много instead of намного before проще?