Learn Turkish: Hiçbir şeyi küçümseme, her şey değerlidir. - Do not belittle anything, everything is valuable.

It comes from the adjective küçük (small) combined with the lesson's suffix -(i)mse, which means to regard something as the root noun or adjective. When adding this suffix, the final k in küçük drops. So, küçük plus -ümse becomes küçümsemek (to regard as small, meaning to belittle or underestimate). The final -me here makes it a negative imperative.

Why is Hiçbir written as one word but her şey is written as two?

This is a common spelling trap! In Turkish, the word şey (thing) is always written separately from the word before it (like her şey, bir şey, çok şey). However, hiçbir (any/none) is a compound determiner that is an exception and is always written as a single combined word.

Why does şey take the accusative suffix in Hiçbir şeyi but not in her şey?

It depends on the word's grammatical role. Hiçbir şeyi is the direct object of the verb küçümseme (don't belittle anything), so it needs the specific accusative suffix -i (with a buffer y). Her şey, on the other hand, is the subject of the second clause (everything is valuable), so it stays in its plain, nominative form.

What is the purpose of the suffix at the end of ?