The Genealogy Mysteries I Most Want to Solve

After twenty-five years of working on my family's history, the following is the information I desire most.

I would love to find what New York county my HILL ancestors (specifically my 3rd great-grandfather, Richard D. HILL and his brother, John R. HILL) left when they moved to Medina, Ohio, in the 1830s.
I would love to find exactly where all of my Irish ancestors (specifically John HANNAN, Margaret (POWERS) HANNAN, James McCORMICK and Margaret (CULLEN) McCORMICK) originated.
I would love to find the baptism information (parents' names) for my maternal grandfather, Anthony DeCOSTA (Antonio de COSTA) from Lisbon, Portugal.

And my most wanted ancestor is...LAU Chung.

The biggest mystery is my maternal great-grandfather. I don't even know what his name truly was, as it was recorded differently on practically every document I have. It was probably LAU CHUNG.

Following is the little I know about him. According to the man [Ling Sang (sp?)] who was the informant on his death certificate, 1) LAU Chong [Chung] was born 03 May 1867 in China. 2) I know he was working as a contractor at Waiakea Sugar Plantation on the Island of Hawaii in 1910. 3) I know he married Maria Augusta CARVALHO 09 Dec 1912 in Kaneohe on The Big Island. 3) I know he bought the lot in the McInerny Tract in Honolulu where he would build their home on 08 Jul 1915 for $350. 4) I know he built that home at 1223 Alani Street between that date and 1916. 5) I know he had three children with Maria: Rose Lyu [LAU], LAU Kui Kyau (known as Hilda), and Alexander CHONG, who was born four months after his father's death. 6) I know he passed away from heart disease 11 Apr 1918 and was buried at Ket On Society Chinese Cemetery in Honolulu. Because of the condition of the cemetery, his grave is likely never to be found. Those few facts and the photo below are the sum total of my knowledge after all these years.

Somehow, LAU Chung was related to a Mrs. HEU FOOK. Her daughter, Emma VICKERY, corresponded with LAU Chung's daughter (my grandmother, Rose) as a "niece" of some order. How he fit into that family is a big mystery. I've pored over all of the documentation and I cannot figure out his connection. It's all insinuated and not specified. The people mentioned by Emma in this letter dated 14 Aug 1964 to Rose were: Dr. William LING of San Francisco and Dr. Leonard LING of Honolulu (Emma's mother's brothers). Her mother was referenced only as Mrs. HEU FOOK in the letter, but I have recently found her birth name was LING See Kyau. Contained in that letter was outdated information from Emma's mother regarding the status of LAU Chung's children, LAU Kui Kyu and Alexander (Chinese name KUI Chong).

With all of his name variations and my not being familiar enough with all of the intricacies of Chinese names and culture, I feel he will always be a mystery.