Strictly speaking 친구 있어요 ? means Friend Have ?

And you would say exactly that for any of these English equivalents

"Do they have friends ?"

"Do you have a friend ?"

"Do you have friends ?"

"Does he have a friend ?"

And so on.

Plurality as a special marker doesn't really exist. Possessive and Article Determiners don't really exist either. Articles don't exist at all. Possessive markers are few and only used when surrounding context might not be enough to convey the needed information.

You might ask, well how would you know which of those equivalents 친구 있어요 means ?

It's context. Korean is highly context dependent. There is no way to tell before reading or hearing the surrounding context.

>Does Korean not have more complex / ceremonial speech patterns?

Oh boy. Let's just say formality and politeness is baked into the language.

Words and sentence/phrase suffixes change depending on your age and relationship with who you're taking to.

친구 있어요 (meaning I have a friend/They have friends etc without the question mark) becomes 친구 있어 speaking to a close friend and 친구 입니다 speaking to someone much older than you (or in a formal setting with say your boss)

There are also on how to address people you refer to in a sentence separate from rules on how you address people you speaking to.