Learn Turkish: Siz bu ürün için herhangi bir garanti veriyor musunuz? - Are you giving any warranty for this product?

While both can translate to 'any', hiç is mostly used in negative sentences or when asking if an amount is absolutely zero. Herhangi bir means 'any kind of' or 'just any'. In this sentence, you are asking if the seller provides any type of warranty, making herhangi bir the natural choice.

Can I drop the bir and just say herhangi garanti?

No, when modifying a noun to mean 'any' or 'any whatsoever', herhangi must almost always be followed by the indefinite article bir. You should treat herhangi bir as a fixed pair when using it before singular nouns.

Why is the present continuous tense used (veriyor musunuz) instead of the broad tense (geniş zaman)?

Turkish frequently uses the present continuous (-iyor) for ongoing facts, current states, or company policies. If you used the broad tense (verir misiniz), it would change the meaning to sound like a polite request ('Would you please give a warranty?') rather than asking about a factual policy.

Why is the pronoun Siz included at the start if the verb already ends with the 'you' ending -sunuz?

You are completely right that the subject pronoun is optional in Turkish. Including Siz here simply adds a touch of emphasis or formality, which is very common and polite in customer service or business situations when asking about a product.