To me, do you need anything? and do you need something? mean slightly different things. If you were going out to the store and you asked if someone wanted something, you could say Do you need anything?, and although you could also say Do you need something?, although it sounds like you're asking if they only need one thing, so it would sound a bit strange. On the other hand, if someone "summoned" you, you may ask Do you need something? but you would not say Do you need anything?. Do the words någonting and något each hold both of these connotations?
Came here to ask this!
"Do you need something?" is something one might say if interrupted by someone unexpectedly (would be a way of saying that you weren't happy about them interrupting you!) or if you were asking if someone needed something specific. Whereas "Do you need anything?" is something you might say to a guest to check they had everything they need or as in the example AlecHirsch1 gives above when off to the store. The phrases are technically interchangeable but definitely can hold different connotations. As Alex already asked - does this phrase work for both equally in svenska?
That's a good question (and I don't have the answer)! You are right, "ting" is an ett-word, so "någotting" (and "ingetting") would make more sense. It is "en ting" in Norwegian though, and there is an old Swedish word "en tingest" which also means "a thing". So maybe "ting" used to be an en-word in Swedish before?