Our museum owns this what I think it Satsumaware Koro. There are signatures on the inside of the lid and on the base. Perhaps someone can assist us decipher the signatures please.
I think you are right about it being Satsuma-ware.
The text in the third picture says 砂金 二両 (sakin niryō), and I think it is saying how much gold was used on the vase. Sakin means gold dust, or gold flakes. Niryō is a value; say, US$2000. But it doesn't look like there would be $2000 worth of gold flake used on that item, so I could be wrong about the interpretation.
The fourth picture says
壽焼 Kotobuki-yaki. Must be a maker's name/mark.
文久年製 Bunkyū nensei. Made in the Bunkyū era (1861-1864)
Bear in mind the marks could be forged, so it would require some expertise (which I don't have) to validate.
Thank you Majestic. Yes you are correct two teals of Gold dust ( ４万円.). Evidently a Chin Jukan kiln product. Agree Bunkyu era (1861-1863). Kotobuki ware seems correct. I am going to try to obtain a larger picture of seal but museum has been moving out so may take time.