Learn Turkish: O çok saygısız biri, ayrıca garsona bahşiş bile vermedi. - He is a very disrespectful person; furthermore, he didn't even give a tip to the waiter.

Yes, you could absolutely use üstelik here. Both mean "furthermore" or "moreover" and are used to add a supporting, often stronger point to what you just said. Ayrıca literally comes from ayrı (separate), giving the feeling of adding something "as a separate/additional point."

Why is biri used here for "person" instead of a word like kişi or insan?

Biri literally means "someone" or "one." In Turkish, when describing a person's character with an adjective (like "a disrespectful person"), it is very natural and common to use the adjective followed by biri rather than kişi or insan. It translates literally as "He is a very disrespectful someone."

Why is bile placed right after bahşiş instead of earlier in the sentence like "even" is in English?

In Turkish, the word bile (even) almost always comes immediately after the specific word or phrase it emphasizes. Here, the emphasis is on the fact that he didn't give a tip (let alone anything else), so bile must directly follow bahşiş.

How is the word saygısız constructed?