"Jeg vil kjøpe et hus."
Translation:I want to buy a house.
It's not wrong, and now added as an alternative.
Keep in mind that while 'vil' can be used to express future in the same way as 'will', we seldom do so without adding some context, because of the ambiguity of the word 'vil' also, and most commonly, being used to express a desire for something.
You are much more likely to see 'vil/ville' used as 'will/would' in conditional sentences, and in sentences where it's already clear that we're talking about the future:
Hvis jeg var rik, ville jeg ha kjøpt et hus.
If I were rich, I would have bought a house.
I morgen, vil jeg jeg ha kjøpt et hus.
Tomorrow, I will have bought a house.
You can express future in more common and less ambiguous ways by using 'kommer til å' or 'skal' instead of 'vil':
Jeg kommer til å kjøpe et hus.
I [am going to/will] buy a house.
Jeg skal kjøpe et hus.
I [will/shall] buy a house.
In another place 'Barn vil lytte' is translated as 'Children will listen'. I'm still trying to figure out how these work.
ah yes, sorry, it's true what deliciae is saying. But if you are speaking to someone, "jeg vil kjøpe et hus" is immediately going to be understood as "I want to buy a house", and you will have to add some specific context for it to be understood as I will buy a house (If you speak it in a shakespearean way for example, as if citing a play). Or if you say "one day I will buy a house" it is possible to say "en dag vil jeg kjøpe et hus". Still it expresses as a wish or desire, and if you want to say that certainly "one day I will buy a house", you should use "skal".
For me "Barn vil lytte" still expresses the personal wish or desire of the one who speaks the sentance, for this to happen. But in general I would always go with "Jeg vil" being "I want", and "I will" being "jeg skal". Barn vil lytte is a bit more difficult for me to explain because I don't know it from remembering the grammar, I just speak and understand my own language. Which is of course not so helpful for someone who is trying to learn it. But I hope this gives some sort of understanding anyway!
Thanks for the clarification! But I was wondering if "Barn vil lytte" could possibly imply the willingness of children, apart from the speaker's desire...