Why is there "have"?
In the sentence "Qu'est-ce que vous avez comme boissons?" (What do you like to drink?), "avez" is in the sentence. I know this is very minor, but I want to understand why and how?
Is this a Duo sentence? (I'm not really caught up on french Duo and just using it as a refresher)
I would translate this sentence more as "What do you have as drinks?" not really "what do you like". But I suppose asking someone what they drink could imply asking their preference for a certain beverage. Asking them what they personally have to drink when they drink, not asking what you may take from them as we would use that phrase in english.
I've noticed Duo tends to use a lot of unusual translations, asking for their implied meaning rather than their literal translation. Makes things confusing.
I think you have misread the sentence. There is no aimer there. It's a question at the bar/to the waitress/at an event about what is available. What have you got to drink/What have you got by way of drinks/What is there to drink? As an English speaker, I would use the verb have too.
Agreed. You have probably found one translation of "comme", which is "like", but it is not the verb "to like" but a preposition. Like me (=the same as me) is "Comme moi". Your expression uses the preposition "comme" to ask "What kind of..." Another example would be "Qu'est-ce que tu fais comme travail?" = What job/What kind of job do you do?
Translations between languages are not always exact. The direct translation for your sentence would be something along the line of "what do you have as drinks"? That could be just the french way of saying what do you like to drink - similar to how they use il fait chaud for the weather is hot. I just saw another the other day where the statement in english was "change your shirt." A literal translation into french would be "change ton chemise". However, the french do not say that. They use "change de chemise" which would be in english "change of shirt".