The Sunday school preceded the prayer meeting, and church historians use the Sunday school as a milestone in determining when the prayer meeting might have started. For example, according to F. Irvin Davis (1908), the first prayer meeting was organized soon after the opening of the Sunday school, while Melva Swartz (1940) reported that the prayer meeting happened at some point during the year following the formation of the Sunday school.
I have only scanned the articles about his resignation as assistant pastor, but the Center Church’s society at first rejected his resignation and even went so far as to offer him the position of senior minister – which was occupied at this point by Joel Hawes, a rather prominent minister in Hartford. Hawes then seems to have taken the hint and retired, but Calkins persisted in his resignation as he had been called to serve in a church in Philadelphia. Both Hawes and Calkins would remain well-regarded in Hartford after this incident: Hawes participated in the examination of Joseph Twichell at his ordination, and Calkins returned to Hartford periodically to preach at local churches.
It’s purely speculation, but the controversy surrounding Calkins’s departure could be related to the desire to form a new Congregational church on Asylum Hill. Church historians always focus on the rigors of reaching downtown churches from the Hill and how that caused church attendance to decline; however, Calkins’s departure, preceded by Hawes’s retirement, suggests that there could have been more going on at Center Church.