Learn Croatian: Kao što sam rekao, svaka igla mora biti sterilna.

You need kao što (meaning "as" or "like") when you are introducing a full clause with a verb, like sam rekao here. You use kao on its own only when placing it directly before a noun, such as kao igla (like a needle).

What is the difference between using svaka and sva in this context?

Svaka means "every" or "each" and always pairs with a singular noun (svaka igla). If you wanted to use a form of sav (all), you would need to make the noun plural: sve igle (all needles).

Does the word rekao tell us anything about the person speaking?

Yes, because rekao is the masculine form of the past tense participle, we know the speaker is male. A female speaker would say Kao što sam rekla.

Why is sterilna in the feminine singular form even though it comes after the verb?

Sterilna is a predicate adjective here. It still describes the subject of the sentence, igla (needle), which is a feminine singular noun. Adjectives must always agree with the noun they describe, even when they are separated by a linking verb phrase like mora biti.