Really strange to use a definite article with no context. It sounds like there is only one song about love.
Well, maybe he only has one in his repertoire? ;) But you are right, changed the default to 'a'.
That's a trap. It sounds like imperative without on or ona. I think they're setting us up to steal our hearts.
But no, that's definitely not imperative, which would be "śpiewaj" (2nd person sg) or "śpiewajcie" (2nd person pl).
There's no "on" because we want to teach you that even 3rd person pronouns aren't needed at all - in real life you have context, so it will probably be totally obvious who the subject is.
Could this also be "he sings a love song" or would you say that differently in Polish?