"I prefer coffee."
Translation:Mám raději kávu.
This is, for the most part, how Duolingo teaches - you encounter new information in exercises, i.e. in sample sentences, and you learn from that. If by "literature" you mean the tips that accompany many lessons, they are bonus information that helps learners to understand things in a more systematic manner - especially things that might be difficult to deduce merely from example sentences.
The verb here is mít, which means "to have" on its own.
The phrase mít rád means to like something, as in to be fond of something (not to like in terms of appearance).
By changing rád into the comparative raději (or more colloquially radši), we get "to like something more/better", i.e. to prefer.
The acutal verb "mít" is conjugated just like you have learned in previous lessons. "rád" is masculine, and "ráda" feminine - e.g. "Máš ráda zmrzlinu?" (Do you (woman) like ice cream?), and "raději" remains the same regardless of gender or number.
What are your questions about the verb "chtít"? It simply means "to want" and it conjugates as follows: já chci, ty chceš, on/ona chce, my chceme, vy chcete, oni/ony chtějí.
Why is it ka'vu and not ka'va? Thx. I believe kavu is the accusative form, but not sure why accusative would be used here or when nominative would be used. I do recall the "Tips" section said they put a lot of the things for this lesson in Food and a lot of things in Animals due to space limitations. As soon as I get through the first level on all the Food section, I will review the Food "Tips" and then also the Tips in Animals. It must have a lot of things explained in those two.
Nominative (káva) is the case of the subject - the "actor" in the sentence. E.g. "Káva je dobrá". (Coffee is good.)
Verbs (like "mít" - to have) need an object. The subject here is "já" (I), even though it's only implied (Já mám rád kávu.) The object is coffee. Accusative is the typical object case, hence "kávu".
Compare with sentences where even English marks cases on words: "I have him." vs. "He has me." --- Both "I" and "he" are nominative, while "him" and "me" are accusative. Same with "Já mám kávu." (I have coffee) vs. "Káva má mě." (nonsensical - Coffee has me) --- "Já" and "káva" are nominative, while "kávu" and "mě" are accusative. And this is really as clear as it could ever get ;)
it's pronounced /ka:vu/, there is not diphthong there.
You can also type both "kávu" (accusative) and "kávou" (instrumental) in Google Translate and listen to the difference.