Great find on the arrival manifest giving her native village.
As to Barbara's last name, yes, that could very well be Uiz. Compare the last letter in her last name to the last letter in Katharine's birth month ("März" = March) - that could be a "z". For a terminal "g", see the last letter in the first word of the last lline ("Zeug." = "witness", abbreviated). The "z" and the "g" in this handwriting are essentially indistinguishable.
As for her father's name, in every entry on that page the last name of the father is left blank and thus is assumed to be the same as the bride or groom's last name. If the bride is a widow, it is explicitly noted - see the next couple in the list, where the bride is "Margar. Hughan verw. Scott" - i.e., Margaret nee Hughan, widow of a Scott (on the previous page in the ancestry.com record I found more cases of brides with "verw."). So, given the conventions of this record, at least the minister conducting the wedding thought that she was not a widow and that her father's name was Nikol. Egler.