Not entirely -- but they are reliable. Based on Metcalf’s recollection that she began the survey after hearing Hawley speak at the City Missionary Society’s annual meeting, October 29, 1860 is the earliest she could have started. Metcalf said that it took her less than a week to talk to every family on the Hill, and four histories of the church (which in some cases may be quoting each other) all place the first meeting regarding the Sunday school in November 1860. The earliest date given is November 4, 1860, which is exactly one week after the annual meeting of the City Missionary Society, and that fits with Metcalf's recollection.
She lived on Broad Street, which in 1860 extended from Farmington Avenue to the Park River (approximate location today: Interstate 84). She moved out of Hartford in 1865.
According to the Courant, nothing. According to Maria Metcalf, he called on everyone to be a missionary, which prompted her to consider starting the Sunday school. According to Atwood Collins, he deplored the lack of a Sunday school in the part of the city lying between Albany avenue on the north and Park Street on the south, and extending from the railroad station to West Hartford and then said “[i] n this district which I have named, there is no Sunday school. There must be 300 children or more who are deprived of Sunday school instruction by the distance which separates them from existing schools. People of Hartford, you must not expect me to do all of your missionary work. I pray you, do some of it yourselves.”
Not sure yet. It seems to have been set up in the 1850s by a coalition of Congregational churches. Its main functions, based on accounts of the annual meetings found in the Courant, were to employ the City Missionary and to provide some coordination among the Sunday schools. Its function does seem to have changed over time, and today it still exists (I think!) as the Greater Hartford Interfaith Coalition for Equity And Justice
It was located on Asylum Avenue, across the street from the American School for the Deaf (approximate location today: Asylum Place).