Translation:A book and a man
As a native speaker, the TTS pronunciation is heard as "Let's stay here with a book/books."
남자 (man) : If we Koreans write this just as heard in Hangul, It will be '남자'
남-(stay in postion) + -자(Let's) : This will be '남짜'
Both words are written as '남자' in orthography.
Korean language has several words for English 'and'.
For 'A man and a woman':
An independent conjunction word '그리고'. If we use this one between nouns, it feel like very formal or poetic and NOT used for neutral purposes.
남자 그리고 여자.
Endings after nominals.
-과/와 : most neutral and used both in speech and writing. 남자와 여자
-하고 : informal and usually used in speech. '하고' is also used as '하-(do) + -고(a verbal ending).
-이랑/랑 : informal and usually used in speech. 남자랑 여자
To everyone: Yes, it's an h, but is is silent sometimes. Duolingo has an explanation for this in the "Alphabet 2" section notes if you are using a computer.
From reading these notes, it says that ㅎ "disappears" before a vowel, but, at least to me, this explanation is not clear. It may be that ㅎ only is silent when it is after a consonant AND before a vowel. I am not sure.
My understanding is that, as in many SE Asian languages, nouns in Korean do not decline by number. So 책 can mean "(a) book" or "books" depending on the context.
I mean, if I said "I bought book," it may be improper English, but you would still understand what I did. And if it's important to indicate how many, I suspect I could use a counter (one book, ten books), or an adjective (like "only" or "many"), but otherwise, it just kinda... doesn't matter.
They don't decline, it's not a declension language, no conjugations, but plurals exist with a particle, but it's the same. The difference is rather in the implicit/explicit plural, as you said, plural is implicit in this language, unless it can't be guessed from the context.
와 is common in writing and only used after a vowel and 하고 is common in speaking and 과 is common in writing and only used after a consonant.
The example you used would be incorrect, according to what I know thus far. 와 means and, but comes after a vowel. 과 means and, but comes after a consonant. So it should be 책과 남자, not 책와 남자. But to answer your original question, yes, you could use 하고 or 과 and both would be correct.
I want to share an excellent comment about the "grammar rules" that Duolingo inconsistently imposes: "@ellablun [...] when a language one is learning doesn't use articles, then translation to english should not enforce usage of particles either. we're not learning english here, so stop molesting us with english grammar. Secondly, if you're gonna force us to type articles, then clarify [...]"
와 = and (attached as suffix to first noun)