A lot of the longer sentences suffer a bit from the fact that it's software doing the pronunciation, however, it's probably good practice for those who will at some point speak Danish with a native speaker. Many Danes are notorious for shortening their words when they speak. For example, "Vil du have et æble?" (Do you want an apple?), ends up sounding like "Ve-du-ha-et-æble?" in every day conversation.
Why is "They cook" incorrect here? Do you need to have an object for the verb to mean "cook"?
The verb 'at lave' doesn't directly translates into 'to cook'. In general it is translated into 'to make' which when relating to cooking nouns/situations could mean to cook/prepare or something like that.
Another sentence could be; 'De laver elektronisk musik' --> 'they make electronic music'. 'De laver bøger' --> 'they make books', which can be considered that they write books, they print books etc.
So it is a bit of a diverse verb which have a direct translation but also could mean other verbs depending on the situation.
I hope I am a bit clear in my response to help you understand 'at lave' better
Yes, thank you. "De laver" therefore would just mean "They make". "De laver mad" is "they make food" i.e. cook.
As far as I know, "they cook" would be "de koger". In sentences like "jeg laver pasta" you could translate it as "I make pasta" or "I cook pasta", but the word "lave" itself doesn't have anything to do with cooking, really. (Native speakers, feel fre to correct me if I'm wrong!)
Well in Swedish the equivalet of "koger" (kokar) means boiling and is restricted to cooking that involves boiling such as (soups, pasta, potatoes, coffee etc).