Inte vs ingen
I know it's not and no, but in english you can say I have no and I don't have a , but can you say "Jag har inte katt" for example, because in the questions it's always with ingen.
Native Swedish speaker here.
When I negate a noun, I normally use ingen/inget/inga.
Jag har ingen katt. (I don´t have a cat.) / Det finns inget kaffe. (There is no coffee.) / Vi hittade inga svampar. (We didn´t find any mushrooms.)
There is also another way to express this (with inte + någon/något/några).
Jag har inte någon katt. / Det finns inte något kaffe. / Vi hittade inte några svampar.
When negating a verb I do it with inte.
Jag gick inte till skolan. (I didn´t go to school.) / Han kan inte hitta boken. (He cannot find the book.) / De kom inte. (They didn´t come.)
Doesn't ingen rather mean none or any?
My Swedish is far from perfect, but "Jag har inte katt" doesn't sound right to me? Is that correct Swedish? I would have thought "Jag har inte en katt" or "Jag har ingen katt".
Are you sure you always use ingen in questions? "Har du inte hört vad hände igår?" On the other hand "Kan ingen förklara vad som hände igår?" It seems to me that both inte and ingen are possible. But I could be wrong. Perhaps my Swedish is even worse than I thought.
Let's get an authentic Swede to clarify, shall we?
I agree although you seem to have clarified it a little bit.
Niej jonm jein soluter.
Actually, the sentence "Vi har inte katt", or for that matter "Vi har katt" is fine. And you can also ask: "Har ni katt?". It probably sounds odd to a learner, but it is an established way of expressing oneself.
https://sv.bab.la/lexikon/svensk-engelsk/jag-har-inte gives a range of example sentences where "Jeg har inte..." is followed by a verb, similar to English "I have not... ". In English, you would not quite say "I have not cat", though you might say "I do not have a cat" or "I haven't got any cat". I suspect that in Swedish, you might have to say something like "Jeg har inte en katt" or "Jeg har inte nogån katt", to make the sentence flow naturally.