There are more knowledgeable people than I, and I suspect the answers to your questions are easy to find on the web and in books. However, since I recall riding the 23rd Street zig-zag of the Second Avenue El at age 5, let me try answers, subject to correction. Try the 6th and 9th first.
See "John F. Hylan" at wikipedia.org
According to some, this mayor was so riled by his early job experience with the Brooklyn Rapid Transit, that as mayor he began plans for the IND (Independent City-Owned System, ICOS) in the 1920's, deliberately to put the BMT and IRT out of business. He paralleled the 9th Avenue el with the 8th Avenue subway, the 6th subway under the 6th el, Fulton St Brooklyn subway under Fulton St El and the Concourse Independent parallel to Jerome Avenue Interborough. His "success" came four years after he died. In 1940, the three systems were "unified," but the 6th, 9th, and Fulton St els were left out of the system. They stopped almost all operation, except for the Polo Ground shuttle and the Fulton el east of Rockaway Avenue.
The major stupidity was the 1942 elimination of the Second Avenue el and the 1950-1955? starvation of the Third Avenue el (cut hours, cut service, claim nobody rides it). Whereas on the West Side, four tracks under Central Park West replaced three tracks above Columbus Avenue, on the East Side six el tracks were lost 1940-1955?, leaving only four tracks on the East Side. It was a 60% loss of trackage.
One link among many:
As for terminals, one might argue, depending on the date. As a generalization, the 2nd, 3rd, 6th, and 9th could reach South Ferry. To the north, probably some 9th Avenue trains reached Woodlawn, though in dad's era I believe the northern terminus was Burnside Avenue. The 6th Avenue route veered west on 53rd Street, just as the D nowadays. As I recall the late 1940's, the Third Avenue had a variety of services (local, express, local-express, and through express), some to Freeman Street, some to Gun Hill Road. The Second Avenue el had a branch across the top of the Queensborough Bridge to Willets Point (and Astoria?) until 1942. Some history book or site will tell you whether and when Second Avenue provided service north of 129th Street. When Dad moved to New York in 1922, he first lodged in Yorkville between Second and Third Avenues. The Third Avenue rumbled all night, but the Second Avenue quit about midnight. He moved the next week to a quieter street.