Please take what I say with a grain of salt as I'm not Danish but we have a similar idiom in Dutch.
"Vil" = "Want"; "du" = "you"; "med" = "with". So the first part literally means "Want you with", by which they mean "Do you want to go with me". The "with me" is omitted as it's clear from the context.
This question implies that the person asking you is about to go to the mall. The question means literally "Do you want with in the mall?" and is to be understood as "I'm going to the mall. Do you want to join me?". Both the verb (to come, to go) and the object (with me, with us) are omitted.
It can also mean "Your friends are going to the mall. Do you want to join/go with them?".
At least this is how it works in German, where the same phenomenon exists ("Willst du mit einkaufen?" = (lit.) "Do you want with shopping?" = "Do you want to go on a shopping trip with me/us/them?").
Oh, right. But if the verb and the object are omitted, context is the only way to know what they are? And if so, I wonder why a) duolingo didn't add it to the tips of the lessons, and b) how we are to know with these sentences that rarely have any context at all. Questions, questions hehe
Possibly. In Swedish we would say "Kommer du med till centret" - the strange thing in the Danish phrase is the use of 'vil', usually a "modal help verb" (is that the expression in English?), that usually only 'helps' other verbs, 'needs' another verb ("Vill du komma med?" = Do you want to come?) -- If this Danish sentence is correct - it is certainly something 'very Danish, idiomatic'.
We have the same in Swedish, 'Vill du in?" Here 'in' is expressing the direction, where we are going 'in or out'. What is strange with the above Danish sentence is the use of "i", which does not work in Swedish, because the verb 'going' needs a direction, and the preposition "i" is about where you 'are', 'being', when not moving. -- And English too, I imagine, since "going to" has 'to' as a preposition of direction.
"Do you want to go to the mall": this is wrong. The Danish says med, meaning with (me); it is not asking whether you want to go on your own. Given this, in British English we would use the verb 'come' rather than 'go': " "Do you want to come with me to the shopping centre?"
If you want to "centre" to mean "the centre point of something specific" like "city centre" you can say "centrum" (and maybe add something to specify what kind of centre you mean.). Or you can rewrite it a bit to say "... i midten af byen." (in the middle of the town/city)
"Vil du med i centeret i centrum (af byen)."