"The artist sings to us."
Translation:Artisten sjunger för oss.
åt very often has the meaning of 'doing something for someone, so they don't have to', that is what Han sjunger åt oss would mean. Like, I can't sing myself so the artist does it for me.
för on the other hand is the preposition typically used when speaking about any kind of 'audience', so it is perfect here.
No, sorry, you can't sing "till" somebody in Swedish. You can "tala till", yes, but "till" is just not used with "sing". Think of it this way: "för" is the audience preposition. You're an audience when he sings to you, not a (possible) conversation partner as when he speaks to you.
'To sing at' would probably mean the singer confronts his audience while singing in stead of gazing at his shoes .. BTW even my English is improving by leaning Swedish: I thought the 'sing to' of Romeo would be reserved for Juliette, which I assumed translates nicely to 'sjunger till' .. but alas, so much for romance.