Short answers, pulled from the story.
Yes. In 1920, team manager Leo Lyons attended the founding meeting of the American Professional Football Association in Canton, Ohio, making the Jeffersons an original member. That organization renamed itself the National Football League two years later, and the NFL recognizes the 1920 Canton meeting as its founding moment.
The Jeffersons suspended operations after the 1925 NFL season. They remained technically suspended through 1927 and allowed their franchise to expire in 1928.
Leo Lyons joined the Jeffersons around 1908 as a teenage player and within two years became the team's full-time manager, financier, and promoter. He represented the club at the 1920 founding of the APFA and later served as an unofficial NFL historian after the team folded.
In late October 1917, the Jeffersons faced the Canton Bulldogs, led by star player Jim Thorpe. Canton won 41-0. Despite the lopsided score, the match earned Leo Lyons and his team national notoriety.
Rochester fans preferred local semi-professional players over the college recruits the Jeffersons brought in. By 1922 the team was caught between being too strong for local competition and too weak to win in the NFL, which drove attendance down. The financial losses eventually led to Leo Lyons losing his house and the team traveling away from Rochester for its final two seasons.
Doc Alexander, a two-time First Team All-Pro selection, played for the Jeffersons from 1921 to 1924. John Barsha played for the team in 1920. The team also tried and failed to sign Red Grange, who instead signed with the Chicago Bears.