Hello Thorby,
Having lived in Germany for nine years, the language is not a problem for me.
Did you obtain those more detailed citations from the German website I had cited, i.e. did you receive an email in German? If so, forward it to me and I shall read the details.
The page that you link to above should provide an explanation of the source HAY, class XLI. However, HAY is not shown on the list.
All the other links take one to another page which states the exact source of the information and provides an address where the information is held. In addition, a standard letter is provided into which one has to merely insert the source and one's name and address.
The IDA goes to great pains to point out that you will most likely have to pay additional fees to obtain the information requested. However, in my experience, German archivists often seem prepared to provide information about Jewish ancestry for free.
Rebecca Baruch cannot even be found in the 1871 census, by which time the family had moved down to Whitechapel. The elder sister, Mary, who would have been 19, is also missing. I suspect that they may have died. Conditions in Red Bank would not have been the most sanitary.
Cheers, Justin