The relation to hemi = half is not correct.
Ethymological Themis is related to CTA, CTACIS, and means something like 'the solid standing'. She is the goddess of justice, but not like
Justitia, but in a more elementary sense of a divine order standing above mankind and all gods.
There were altars in
Delphi, Olympia,
Thessalia,
Boiotia, Attika usw.
Identified by the
Romans often with Carmenta or Carmentis, an ancient
Roman deity with nearly unknown nature.
Out of my books!
But I think no
help for your questions anymore!
Regards,
Jochen