I would think that Bulan apa saat ini would also be acceptable. Is there a semantic difference between saat ini and sekarang?
Bulan apakah sekarang or Ini bulan apa? Are both valid. The answers need to evolve
Would 'Bulan sekarang apa?' work as well?
No. It's better "Sekarang bulan apa?"
Why not 'apa bulan ini?'