Why does Lady Kumaria look like Sumika?
pixiv encyclopedia (Japanese) claims, 


  Whether Sumika was the goddess (Lady Kumaria) in the first place or the goddess appeared as Sumika in response to Kureha's mental state, it is not stated within the story and hence, it's left to the viewer's interpretation.
  
  (Emphasis mine)


TV Tropes (warning!) also describes it as:


  
  Ass Pull: Sumika being Lady Kumaria. Never foreshadowed, comes out of nowhere, never explained and serves as a mechanism so Ginko and Kureha can get together.
  
  
  Or maybe not. It's never explicitly stated that Sumika is Lady Kumaria and it's more than likely that she simply took on that form as a symbolic representation of what Kureha learned from Sumika.
  
  They Wasted a Perfectly Good Plot: Quite a few, for the same reasons as listed in They Wasted a Perfectly Good Character.
  
  
  Sumika being a part of Lady Kumaria, which is never explained. There's also the fact that she apparently knew she was going to disappear or otherwise leave Kureha one day, which (though it may connect to the first reason) is also never explained.
  
  
  
  (Emphasis mine)


which all the possibilities have been mentioned in the question itself.

As of now, there is no official explanation why Lady Kumaria looked like Sumika... which leaves us only to fan theories (which are omitted in this answer).

P.S. considering that there are even fewer discussions about this issue in Japanese, I conclude that there's really no official statement as of now.