That's often correct in English, Arnauti, but I wouldn't ever say the question/negation way is always the rule. A quick example would be the common question, 'Do you have something for me?' Or 'Do you have something in mind?'
'Anything' and 'something' are so often used interchangeably as pronouns, but not always, depending on situations like if the noun is finite or infinite in extent or amount, or on how polite you want to seem.
e.g. 'Do you have something/anything (for me) to eat?' 'No, sorry, I don't have anything.'
Just for those here also learning English, maybe a decent reference, since this is strange to explain in English:
I agree that it is English that is odd. :D
Yes, I agree that my rule was overly general. The explanation with how determinate/specific the thing is is much better. – The level of politeness follows from the fact that it's more polite to offer an unlimited range than a limited range, so that's just a contingent effect.
Thanks a lot for the link to this. I know many of our students aren't native speakers of English, so we sort of get the task of teaching English too, but our focus tends to be on Swedish grammar :)