You are asking legitimate questions to locating this family. It's just that it takes more time than I have to contribute, at this time.

The very best next steps, in order of importance, are:
l) Track the family in Queens County Directories. Perhaps you can email the Library Director at
Queensborough Library, about your project and reasons, and they might be willing to provide you look ups on Otto and his parents. (Many immigrants arrived in and stayed in NYC, then moved to
Suffolk, and Nassau counties from Queens...some moved to New Jersey and some to Westchester County later.) A chronological search of directories would provide you with place and time.

2) You need the marriage records of children, to confirm they are in fact relatives. These are held at NYC Municipal Archives. Someone would have to go there to view them to confirm names of parents.

3) Perhaps the same library might do a search for Obituaries of Otto's parents, which would be
key to names and locations of descendants.

As for Kach and Roch it sounds like they are US census records misspellings.

The surname KOCH is Jewish and Christian in NYC. This interferes with searching church records. NYC has the 2nd largest worldwide Jewish population, 2nd only to Israel.

If you search US Military records, this may provide more in formation.

I hope these generic responses may help you.