Hyakkimaru's mother prays to a statue without a head. What is this statue without a head?
The statue that Hyakkimaru's mother prays to is Goddess of Mercy. The Goddess of Mercy statue had a head before Hyakkimaru was born.
"The Goddess of Mercy statue sacrificed its own head at Hyakkimaru's birth so the child would not lose his head in his father's bargain with the demons.", (Reference - Notes, en.wikipedia.org/wiki/Dororo_(2019_TV_series))
For more summarized details about the episodes you can refer to following link : en.wikipedia.org/wiki/Dororo_(2019_TV_series)
The statue actually is called guanyin goddess. The statue orginal have a head but the goddess protected Hyakkimaru and it cost the statue head blast off. Actually it was just a guess from a youtuber. I'm not sure the explanation is correct but here is a link to the video. The explanation start at 4:07.