There is no easy way to find the answers to your questions. Early birth records in New York were initiated and filed in the Town Clerk's office. You'll have to find the name of the town where he was born and contact the Town Clerk.
I'd look for Jeremiah and Phoebe's marriage license. Both sets of parents names might be on it. If not, then look for the newspaper announcement of their marriage.
Their parents names might be in their newspaper death notices.
From looking at the 1870 Wayne Co. Census, it looks like they may have died there.
I'd contact the Lyons heritage Society, https://lyonsheritagesociety.org/
, Lyons Public Library, https://owwl.org/local-history-resources
and ask if they have a local death index, indexed newspaper death notices and cemetery inventories.
If they don't, I'd contact the Wayne County New York web site, http://web.co.wayne.ny.us/office-of-the-county-historian/
who does have a surname database, public records and cemetery info.
Early Wayne County newspapers are on microfilm at the New York State Library, www.nysl.nysed.gov/nysnp/159.htm
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