(At least) dreams as ambitions and goals. I think the ones we have when sleeping is sen.
Aren't "marzeń" really more like imaginings or daydreams? I'm pretty sure they aren't dreams while sleeping.
This is very much a colloquial or dialect way of speaking. It is not grammatically correct.
I think it's the usual way of speaking in Britain. Nothing "grammatically incorrect" about it.
Though I can't speak for the whole of the UK, I never heard She hasn't got dreams in any region I lived in. It may be regional; it's certainly not "the usual way of speaking in Britain". Often heard:
She has no dreams.
She hasn't any dreams.
She's got no dreams. [with got, which British teachers taught us to avoid!]
[28 Feb 2019 14:29 UTC]
I was always taught "have got" to be a common (although of course less common) equivalent of "have", so "She hasn't got (any) dreams" would be a very natural phrase for me...
So marzeń is a plural? I can't see why 'She doesn't have a dream' is wrong. :(