Part I: I didn't find the link to Calvin. Appears that Sylvester descended from William W. Partridge and Louisa Edwards; and that William W's parents were William and Elizabeth.
History of the town of Duxbury, Massachusetts: with genealogical registers
By Justin Winsor
Partridge: (8) Calvin, b. May 29 1739.
Col. Calvin s. of (5- Isaac) Duxbury m. Mary widow of Col. Ichabod Alden, Oct 24, 1779. He d. Nov. 27, 1815; had John Nov. 22, 1781, m. Elizabeth Delano of M., who was b. Sept .30, 1788, and had Elizabeth, Lucretia ,Ruth, Mary, and John; Ralph, Nov. 13, 1783, m. Hannah Sprague; had Almeda 1815, m. Wm. Ellison, Ralph 1816, d. at sea 1836; Wealthea L., 1821, m. Capt. Ebenezer Howes, George Leroy 1829; Mary Dec. 10, 1786, m. Nathl Soule Jr ; Rebecca m. Constant Sampson; Ruth Hannah Dec. 12, 1792; Ichabod Alden May 1, 1798.
Massachusetts, Births
https://familysearch.org/pal:/MM9.3.1/TH-267-12390-47701-97?cc=1536925&wc=11695119
Joseph M Partridge
Birth 08 Oct 1851 Roxbury, Norfolk, MA
registration date: 1851
registration place: Roxbury, MA (p 221 no. 508)
father: Sylvester Partridge Coachdriver birthplace Northhampton
mother: Sarah E birthplace Maine
Massachusetts, Marriages
https://familysearch.org/pal:/MM9.1.1/N43W-5JL
name: Joseph M. Patridge
Residence Boston Highlands
Occupation Butcher
Marriage 07 Nov 1872 Beverly, Essex, MA
Male age: 21 est birth 1851 Birthplace Boston Highlands
marital status 1st
father: Sylvester mother: Sarah
Marriage 07 Nov 1872 Beverly, Essex, MA
Marriage registration year: 1872
Marriage registration place: Beverly, MA (p 189 no. 74)
Official Rev. S Jackson, Boston Methodist CH
spouse: Mary E. Lowe
Residence Beverly
Age 21 est birth 1851 Birthplace Deer Isle, MA
marital status 1st
father: Nathan mother: Hannah
https://familysearch.org/pal:/MM9.3.1/TH-266-12428-16330-25?cc=1469062&wc=6961484
Sylvester E. Partridge
Omnibus driver
Male age: 32 est birth 1818 Birthplace Northhampton
marital status 1st
father: William W. Partridge mother: Louisa
Marriage 20 Oct 1850 Roxbury, MA
Marriage registration year: 1850
Marriage registration place: Roxbury, MA (p 184 no. 156)
Official Rev S B Croft (?Craft) Boston clergyman
spouse: Sarah E. Harriman
Age 22 est birth 1828 birthplace South Pomfret
marital status 1st
father: John Harriman mother: Avis
Massachusetts, Births and Christenings, 1639-1915
https://familysearch.org/pal:/MM9.1.1/FHFB-V86
Sylvester Edwards Partridge Male
birth 11 Jan 1818 North Hampton, Hampshire, MA
father William W. Partridge
mother Louisa Edwards Partridge