Short answers, pulled from the story.
Hitler postponed Operation Sea Lion indefinitely on the 17th of September 1940 because the Luftwaffe had failed to defeat the Royal Air Force and was suffering mounting losses in the Battle of Britain. The precondition in Führer Directive No. 16 required the RAF to be beaten down before any Channel crossing could begin, and that condition was never met.
The finalised plan called for nine divisions to land along four beach sectors on the south coast of England, running from Folkestone and New Romney in the east to Beachy Head and Brighton in the west. A single airborne division was to land in Kent, north of Hythe, to seize the aerodrome at Lympne and bridge crossings over the Royal Military Canal.
The Sea Lion plan called for approximately 138,000 men to be ashore within the first two days, rising to 248,000 within the first fortnight. The first echelon alone was to consist of around 67,000 men landing across the four beach sectors.
The Kriegsmarine was severely weakened by the Norwegian campaign, after which it had only one heavy cruiser, two light cruisers, and four destroyers available for operations. More than half of Germany's surface fleet had been sunk or badly damaged in Operation Weserübung, leaving it hopelessly outnumbered by the Royal Navy's Home Fleet.
Tauchpanzer were Panzer III and Panzer IV tanks made fully waterproof by sealing all hatches, sighting ports, and air intakes, allowing them to walk along the seabed. Air reached the crew through an 18-metre rubber hose attached to a surface float, and navigation was by gyrocompass or radio from the transport barge. By the end of August 1940, Germany had converted 160 Panzer IIIs and 42 Panzer IVs to this configuration.
Germany lacked purpose-built landing craft and converted approximately 2,400 inland river barges collected from across occupied Europe. These were modified with bow openings, internal ramps, and concrete floors for tank transport. Several specialised variants were developed, including concrete-armoured assault barges carrying ten small assault boats and barges fitted with surplus BMW aircraft engines for independent propulsion.