Short answers, pulled from the story.
A total of 709 Type VII submarines were commissioned between 1935 and 1945, making them the most produced submarine class in history. The vast majority were Type VIICs, with 577 built at fifteen shipyards by the end of the war.
The Type VII was designed to attack Allied convoy lanes in the North Atlantic using Karl Donitz's Wolfpack tactics. It formed the backbone of Germany's effort in the Battle of the Atlantic and also served in the Mediterranean, Arctic, and American waters.
Germany circumvented the ban by establishing a Dutch front company, NV Ingenieurskantoor voor Scheepsbouw Den Haag (IvS), which continued submarine design work in secret. IvS built three submarines in Finland in 1931 before Germany began openly ordering Type VIIs in January 1935.
Most surviving Type VII U-boats were scuttled by their own crews in Operation Regenbogen. The British disposed of the remaining boats in Operation Deadlight. A small number entered foreign navies, with the last one decommissioned in 1970.
The only preserved Type VII submarine is a VIIC/41 on display at the Laboe Naval Memorial in Laboe, Schleswig-Holstein, Germany.
The main subtypes were the VIIA (ten built, 1935-1937), VIIB (twenty-four built, improved range and armament), VIIC (577 built, the dominant variant), VIIC/41 (88 built, stronger pressure hull), VIID (six built, SMA minelayer), and VIIF (four built, torpedo supply submarine). The VIIC/42 and VIIC/43 were cancelled before any were commissioned.