"Did a bird just chirp?"
Why are we using 今 here? Isn't 今 now? This sentence is in the past tense, right? Can anyone please clarify my confusion?
Using ばかり or ところ here doesn't sound correct because it puts the emphasis on the time since the chirping; therefore it makes it sound like you're asking if it was just now that the bird chirped.
You could maybe use たった今 to put an emphasis on the "just", but it's really not necessary.